Look at how the sports that already separate based on non-gender-classes do it and adapt as needed. Look at Boxing, as noted, and at something like Baseball, which has major and minor leagues separated by skill level.
And although pound-for-pound women are physically weaker than men, they also have greater endurance, so would have an advantage in contests that focus more on endurance than brute force.
Just like boxing classes exclude smaller, weaker men from the more popular heavyweight tournaments.
Women are already effectively excluded from top-tier tournaments, since the most popular are those on the most extreme end of the performance scale, and are almost entirely dominated by men. There are tournaments specifically for women, but aside from a very few sports such as gymnastics, which focus more on precision than brute strength and endurance, none are as popular as their male counterparts.
I can see a few issues that may be dealbreakers.
For one thing, it doesn't scale. Differences between boys and girls are going to manifest easily as early as middle school. And I think it's unlikely that schools and independent town organizations will have the resources to manage however many tiers and subdivisions it would take to include girls in things like basketball at anywhere near the level that current sex segregated teams currently do.
I can really imagine it going more or less only two ways in school athletics. Either girls are largely classed out of the available tiers of play, or whatever lower tier there is gains an unspoken reputation as the girls tier and boys would not apply to play in it for the most part.
I can't see that as much of an improvement.
That's at least true for team sports that require resources. Perhaps in some sports it might work out, but certainly not in the major most popular sports.
And then we get to the psychological effects. While people can indeed be very excited to be the best in tier 12, it's certain to dim enthusiasm if that's the best fully half the population can hope for. We're all aware that sex segregated sports exist because men and women aren't competing at the same level, but quantifying exactly how much lower the women's level is, and identifying the levels they can reasonably compete in by labels that specify how much lower they are then the top is going to seriously kill the excitement.
This all brings us back to the problem we're trying to address, trans athletes. Trans people are a very small population. That's not to say we should ignore their interests or feelings, just that effect size should be taken into consideration.
Out of the already tiny trans population, the roughly half who are trans men don't pose any competitive issue. Their female sex does not confer any advantage in men's sporting competitions, so if they're at a level they can compete, good for them! The easy solution is to let trans men compete with men.
As for trans women, we're down to a very small number of people. Then an even smaller part of that group would like to compete in women's athletics.
We're looking at a rounding error. To say that we upend the entire organizational structure of sports in a way that negatively impacts a far larger number of women for a miniscule number of people- whether or not you or I think it's a good idea, it will not actually happen.