It's only the adults who care about records
How do I know you weren't a jock growing up? Every single guy I know who played HS football (or girl who played soccer or softball, or ran track...) can tell you what their team record was, if they won the Championship, or if they were undefeated, or if they never won a game, every HS jock, male or female can tell you if they set a state record when they were playing - and they are going to know that, as my friends do, 40-50 years after they actually played those games, or set those records. I skied downhill competitively in the FWSA in HS. That was back when Nixon was President. I can still tell you my ranking for every one of those 4 years. I can still tell you the winning time from the one and only race I won in those four years (I tended to place a steady 4th/5th, but did OK in the overall because I did do it steadily, other people won big or crashed and DNF).
I'm sure, like many schools do, there was a wall in our gym that had all that information listed, who held what school records, what championships were won, who holds what state records. You're not going to forget your name up there. Hell, I go back to watch games in that gym and my eyes always look at the banners we won (3 conference championships in football, 2 in basketball, one Top of the Bay Championship) when I was there - yeah, 40 years ago, plus.
So people really, really care about records. Not just adults.
... and they're children /// They all get to play any sports they want
Well they are not, and they don't. They obviously (it's the point of the story after all) not getting to play any sport they want, as sports on that level are being cut due to catastrophic budget cutbacks in most areas. And, for a lot of these kids it's pretty serious stuff. It's serious on the level of their interpersonal stuff - and, more importantly - in stuff like college scholarships. Whatever gg just lost the chance to be the state champion may well have lost a scholarship in that process also.
If you know of "easy ways to make sure each side goes up against their own gender," then please submit those ideas to the public school systems.
It wasn't even a serious question until a decade ago now, and they are going to have to follow the lead of international sports - which, like it or not - is going to end up being genetic testing
One of the key things that makes sport 'sport' is that a huge amount of effort goes into making sure the game is as 'fair' as possible for both sides so it ends up being a contest of skill as opposed to luck. And there is no way to 'fair up' the differences in between teen age boys and girls for most sports. My female friend Pooh (yeah, that's what everyone called her), was a much, much better skier than I ever was, but as good as she got her downhill times were always just a touch (a couple of seconds at best) behind mine, even though she was skiing better, that 50lb difference between us was all but impossible to overcome given the basic physics of the event. And in a sport where times were split down to the 1/10 of a second (1/100 now in international competition) a couple of seconds is forever.