In this post, which I am glad that FOMG is courteous enough to allow me to share, I plan to address three questions. Firstly, what should Latias run in ADV OU, if it were freed? Secondly, how does Latias affect the metagame? And thirdly, should Latias be freed? Obviously my answers to these two questions are not the final word on th matter, but I have thought about both enough that I hope to shine some light on the topics and ensure people need not spend time on the simplest advances, but discuss the topics on higher terms. At the end, I will provide a sample team.

A) What should Latias run in ADV OU, if it were freed?

Blissey, Jirachi, Snorlax and other top Latias checks are already very popular in ADV OU, and they are notable for having significant staying power, and aren't necessarily easy to trap either. With that, it's hard to make the case that Latias should pretty much ever drop Recover. It is not even worthwhile to drop it in favour of running RestTalk, as Recover + Refresh is far superior.

The next question then is what sort of set are you running - a more supportive, or offensive set? For support sets, you do have a lot of useful options - Thunder Wave, Light Screen, Roar and Wish are all interesting, certainly. For offensive sets, Calm Mind is pretty much a must. It's not an unheard of proposition that you could run 3 attacks and recover, but the ability to boost offers so much more to Latias than further coverage. That is because Dragon STAB (using Dragon Claw) is such an excellent STAB option, with only Steel-types resisting it. Psychic-type attacks are almost worthless on Latias; the only relevant Pokemon you hit harder are Fighting-types (like Heracross and Hariyama) and Poison-types (like Gengar and Venusaur), so to the extent that it has any use at all, it is to surprise a certain small set of Pokemon, none of which really act like checks to it anyway and all of which are hit neutrally by Dragon Claw.

That puts us most of the way there to what, in terms of move options, offensive Latias should run: Recover, Calm Mind, and Dragon Claw. The remaining slot should be dedicated to beating the Pokemon that check and counter a set running just those moves. The most notable of these are Tyranitar, Blissey, Jirachi, Metagross, and Snorlax. It's not a complete list and some teams will rely on more niche Pokemon, or rely on stuff like fast revenge killers or other tactics to take it out, but they're the main Pokemon to be concerned about in crafting a set. Tyranitar and Snorlax aren't really Pokemon you have many options to make Latias more effective against, although Surf is an option that helps versus Tyranitar. As Surf hits Steel-types neutrally, it's not an unusable option, but there are better options against Steel-types. For Jirachi and Metagross, Hidden Power Fire is your strongest option against them, while Thunderbolt or Thunder is an option that hits them both neutrally and hits Skarmory too. For Blissey, Refresh is a serious option to consider. Although Refresh Latias has a much harder time beating Steel-types, it is able to beat all variants of Blissey except for the rare Snatch variants (which only exists really because of the existence of Refresh Latias, and frankly even then isn't that viable of a set), and can help versus defensive variants of Jirachi too (though I would still be worried about Body Slam variants). Roar is an option you can try on defensive latias too in tandem with Spikes, but it doesn't help with Latias' vulnerability to status. Finally, don't bother with Ice Beam on Latias: Dragon Claw is almost entirely superior. Dragon+Electric coverage is better than Ice+Electric coverage when you have Dragon STAB.

Beyond movesets, EVs of course need to be considered. Latias has the same base speed as Gengar, so notable speed benchmarks include outpacing Adamant and Jolly Heracross, neutral and +speed base 100s such as Zapdos, Salamence, and Flygon, and of course opposing Gengar. There are benefits to outspeeding each of them, as well as to having more attack power or for increasing its bulk. I'll let you guys play around in the calc and see what you find.

Tl;dr:
Run CM + Recover + Dragon Claw + HP Fire/Refresh on offensive Latias, for defensive latias run Recover + Dragon Claw and then 2 support moves or a support move and a coverage move, with good options including Thunder Wave, Light Screen, and Roar being among the support moves worthy of consideratios.

B) How does Latias affect the metagame?

Latias is a strong, ground-immune and difficult to effectively trap Pokemon which acts as a good check to many of the Tier's Water-, Electric-, and Dragon-types. For most archetypes, it gives as well as takes away. For example, for physical offense, it provides an excellent switch in to swampert, but it doesn't really hurt this sort of team at all as Latias isn't an effective check to any physical attackers beyond Flygon and to a limited extent Salamence. For CM Spam, a rare archetype as it is, while it is an issue for those sorts of teams as it makes life difficult for some CM abusers, it also quite clearly provides them a new and powerful tool to play with, so if anything it ups the potential for that sort of team. For balanced and stall-type teams, it provides a new check to a number of threats, which can offer support or act as a win condition, as the team sees fit. And Latias, while immune to Spikes, providing a new tool against Gengar Spikes teams, is also a good abuser of Spikes (and trapping) itself, so it both gives and takes away for those sorts of teams too. It should also be mentioned that one of Latias' big flaws is it is set-up bait for DDTar... Latias is good, but it is also set-up bait for the best sweeper in the tier.

I feel like the Pokemon which take the biggest hit from Latias being in the tier are Swampert and Moltres. Moltres is already a niche Pokemon as it is, but having a commonly featured and very good answer to it is kind of a bit of a death knell for it. Swampert finds that it is far easier to be pivoted into, though it is lucky that the teams that Swampert finds itself being most useful against (physically offensive teams) are also a sort of team where Latias doesn't find itself a natural addition (since it has a very different set of checks and counters to most members of physically offensive teams anyway). While offensive Electric-types take something of a hit, it should be noted that Refresh-less variants of Latias absolutely hate being paralyzed, and a paralyzed Latias is actually pretty easy for Electric-types to bust through, especially with the assistance of sand, so it's easy to overrate the hit that they actually take from being included in the tier.

C) Should Latias be freed?

Before I argue about whether or not Latias is in any way shape or form broken, the first thing to do is to provide some historical context to the ADV OU tier, and to note that the question about whether Latias should be freed rests not just in the question of the extent to which it is or isn't broken, but also on whether the tierlist should be kept as is for the sake of the tier's legacy and history. How to value those things is up to you, and while I have a fairly firm stance on whether or not Latias is broken, and whether it should be included if the decision were based only on that, it is most definitely not for me to decide Smogon's tiers and for me to decide how to value its history in the context of the modern philosophy applied to tiering.

As I said, first some historical context. The history of ADV OU tiering is actually rather fascinating and bizarre, and far less clean than people make it out to be given the dramatic situation of Garchomp in DPP - we all know how that went.

At the birth of ADV OU as a tier, things were actually rather different in some ways versus how they are now. Among other things, Wobbuffet and Wynaut were legal, and before FRLG were released, a lot of Pokemon weren't legally obtainable in game. But perhaps most significantly to the point I wish to make, Celebi and Jirachi weren't legal in ADV OU initially either. (Citation: "Believe it or not, Celebi started out banned in the Advance metagame (back when it was held on the IRC-based RS Bots). When the NetBattle crowd unbanned it (along with its partner in crime, Jirachi), this was a major breakpoint between the two communities." - https://www.smogon.com/smog/issue10/adv) In essence, Celebi and Jirachi, two top Pokemon in ADV OU, were freed at the whim of the owner of Netbattle. My understand (though I can't, after significant searching, find a thread telling me one way or the other) is that Wynaut was banned alongside or soon after Wobbuffet because it was seen as being broken in UU. If my memory serves, I think I remember seeing that in a thread involving david stone.

I would make the argument, having played a fair number of games in ADV OU + Latias, that Latias is not even as good as Jirachi in the tier. Furthermore, I'd make the argument that, had Latias been freed (without Soul Dew, of course) alongside Jirachi and Celebi today, we would consider it crazy that anyone should suggest it to be banned and certainly not consider it the best Pokemon of ADV OU. That is, of course, not the world we live in now, but I think it is something that people should seriously think about. Furthermore, I hope that people take this historical context into consideration when evaluating the importance of preserving ADV OU's tier list in its current form for history's sake.

D) Sample team: https://pokepast.es/f13e4fb422a0bee5

I found it surprisingly difficult, actually, to build a decent ADV OU + Latias team which actually includes Latias besides the obvious team pasted above. The sets I went for probably aren't the best and reflect both how out of step I am nowadays with ADV OU and my own teambuilding tendencies to a degree, but the important thing to think about if you do choose to adjust the team is to note that Tyranitar, Blissey, and Skarmory all act as checks to Latias in some way. Latias has obvious synergy both with trappers and with other Calm Mind users, but I often found when attempting to construct other teams with Latias that it left me with gaping defensive holes. I am interested in seeing who can do better, and come up with a more creative Latias build than the one above which is nonetheless well-built. It is a harder challenge than it appears! I should note also that most ADV OU teams are viable in ADV OU + Latias too, just obviously check you have a plan for the common potential variants of Latias, and are able to pressure it offensively or handle it defensively.

E) Replays: https://replay.pokemonshowdown.com/search/?format=gen3oulatias

I have played a few games of this with other competent ADV players and saved some of the replays. You can find them through the link above. I would highlight the tournament set I played with Cowboy Dan, for a tournament hosted I believe by Marcop and Altina:

g1: https://replay.pokemonshowdown.com/pokemonperfect-gen3oulatias-4305
g2: https://replay.pokemonshowdown.com/pokemonperfect-gen3oulatias-4306
g3: https://replay.pokemonshowdown.com/pokemonperfect-gen3oulatias-4307