I think one of the problems is spotting talent.
My dc at state school did PE as in 8 weeks of lessons of one sport then onto another.
That was 16 lessons. The first lesson was always non-practical talking about safety and equipment. The last lesson was always fun/sorting out going onto the next lesson. There was also a very high chance that at least one lesson would be rained off/have a trip/teacher away. So I'll call that 13 lessons. 13 hours.
Except realistically with changing maximum of 40 minutes a lesson, so let's call that 9 hours.
In 9 hours, with a group of keen pupils and a specialised teacher... I doubt many would get to the stage of either thinking "this is fun. I want to do more" or "I'm quite good at this."
In 9 hours in a lot of sports you're not really even at the stage of being able to do a proper game.
So you're looking at getting talent from out of school clubs. And barring a few, the children need a parent who is willing to take them, and pay for equipment.
So by this point, you're really reducing the number of children you're looking at to discover talent to a relatively small percentage. Even if you find talent in the club, a parent may say they're not interested (yes, I've seen that, with a coach offering free lessons because they saw huge talent).
From a non-sporty child's prospective (as me and my girls were) the 8 weeks then move on is lovely. Not too much is expected. Any hated sports are over and done with quickly.
But from a sporty child who has potential but not got parental support to do it outside school, it's not going to inspire them enough, or is someone going to coach them to find they're quite good.
My dad was the latter. He is very sporty, and at his secondary modern they did a term of cricket, a term of football and a term of rugby. He was captain of certainly the latter two, and I think played for the county for them all. His parents could not afford the bus fair to get there so he used to walk several miles to play. They certainly couldn't have paid for equipment or club fees.
I sometimes wonder whether if he'd had the money for proper coaching and equipment etc how far he'd have gone. Today it's even harder.