Hey, I know I'm not around much but I wanted to throw out my thoughts as someone who has been on the fringes of the community for over a decade now. I've sadly not been able to do runs for a good number of years due to serious hand pain issues, though I try every couple.
I'm generally fairly liberal with accessibility aids and input assistance due to my own issues, though I'm a purist when it comes to what constitutes a run. No premade files, any% is always unrestricted, no external software tools, a timer should never be paused during a run (aside from unmanipulatable load removal to increase consistency of competition for players) - that sort of thing.

Personally, I don't think intro skip is a good idea, due to a combination of established competition and the fact that asking what is and isn't part of a game will always be contentious.

Leaderboards and communities of any competition agree on rulesets for fair competition above all else. Rules are generally set as an agreed upon standard to which everyone agrees for the sake of that fair competition.
I personally separate rules into two distinct types - Rules that define what the competition is, and rules that define how the competition is held. The first type is very simple, basically asking the question "What is the competition". What is the game, how does the timer start, what do you do, how does it end. The second type is a bit more complicated, with specific regulations on platform, tools, banned tricks and glitches, etc.
Two points of contention that could be had that fit into the first type of rule are "What is the start", and "What is the end". The reason this needs to be defined is solely to create a consistent and level playing field for every competitor, with no room for any grey areas. For a long time in this community, this has been agreed upon as the start being the button press to load a newly created file, and the end being losing control of link and the credits running. Obviously this is not the case in all speedrunning communities, a lot of Japanese communities and the TAS community famously time from console power on until last input. Both of these methods are perfectly valid, so long as they are applied consistently.

Having established this, with regards to Plan A, any sort of timer manipulation at the start fundamentally undermines that competition. There are now two entirely different standards for what constitutes the start of a given run, and that fundamentally undermines the very nature of what the competition is.
In addition to the objective gameplay difference of the text mashing and exiting of Link's house between the two timing methods, there is a very, very big difference in playing the intro vs not in terms of your own mental state. Having to sit through the intro is a very real part of the run, as it adds further risk to the early game. Restarts not being immediate means the risk of doing harder strategies is higher due to the real life time loss incurred, and that is *very* much a part of the run to me. If the intro is skipped and riskier strats are implemented, it's unfair to compare this competition to the competition with the intro.

To that end, the only truly fair method to implement Intro Skip is with Plan B, entirely skipping it and having all players start on a consistent and even playing field. This shouldn't be something that people can pick and choose, it very much should be a standard set for the whole community as a core basis of competition.
Changing the basis of competition isn't necessarily bad on the whole. In athletics, most track events changed from imperial measurements to metric, upending a century of tradition and competition. However, it does fundamentally change what that competition is. The mile run might have been replaced by the 1500m, but the record times for the mile weren't converted over as it was a fundamentally different competition.
My main issue here is that older runs cannot be retimed accurately under this system. We're altering the start parameters due to Link's starting position in his house, and due to this it's impossible to retime old runs while keeping things *exactly* fair. From my perspective, the only way of doing this fairly would be to start timing from fadein after leaving Link's house, but then we're skipping gameplay and I'm sure that would be even more contentious.

To sum everything up, I don't want the intro gone.
I don't think Plan A is viable at all for fair competition. Plan B could be viable, but only If the load of a save was able to get the game into a state exactly as it was after watching the cutscene. I'd not want it since skipped runs will always have an advantage, but I'd not speak against it. However as things are, both of these options fundamentally change what the competition is, and neither of them provide a truly fair platform compared to historic runs.
To me all facets of a game are relevant, both good and bad. Would it be a better speedrun without the intro? Probably, yes. But it wouldn't be the same speedrun.