Starter-counterpick dichotomy is bad for two reasons:

1. Strategically, it's incorrect to ever practice or choose any stage that is not legal in game one. Think about it. If your general play strategy is designed to win on the starter stages, you can counterpick starter stages for a hypothetical game 3 and win 2/3 games in a set and thus win the set. If your strategy is optimized to winning on counterpick stages, you win only your own counterpick for 1/3 game wins and a set loss. We've seen this in every previous Smash game. Top players virtually never counterpick cp only stages, and this is why. Strategically the cp only stages are effectively banned, and in reality, stages that are always incorrect to choose will be banned in practice eventually too which is also what has happened in every previous Smash game. This is the road to the Smashville metagame.

2. You have to decide which stages are starters, and there's no good reasoning you can use between generally legal worthy stages for which are somehow "more" legal as starters versus "less" legal as counterpicks. It's obviously not based on match-up polarization; we have had one of the most match-up polarized stages, Final Destination, as a starter every time. There are no real features you can point to, and we have like 15+ flat + plat stages already existing in Smash Ultimate anyway. It's a totally arbitrary decision that basically amounts to "the whims of the TO today" because in reality there is no possible objective standard you can use. This is really problematic because any arbitrary decision will have major winners and losers, and the players who mained the characters who excelled on the perfectly fine stages we banned for no good reason will rightly feel cheated and will reasonably feel a lot less interested in continuing to participate in events.

So that's your main problem right there: you have 20+ good legal stages and it's totally not a reasonable or viable option to select only a handful of starters assuming you approach the game with the outlook that banning things that aren't ban-worthy is inherently unacceptable (some people legitimately don't agree with that statement and believe they should just pick a few stages and don't care about what's lost, but I don't share that view at all). I think it's obvious that with 20+ stages legal for game one that the 3-2-1 solution relying on RPS would collapse into extreme unfairness so I won't go into the explanation of why unless it's requested