It seems like everyone wins in that scenario, it's healthy but playful and low stress while accommodating parents' need for scheduling.
Is such a thing common? I don't hear about it much.
Middle school and junior varsity high school sports coupled with math tutoring is probably enough to keep them busy enough and out of trouble/off social media.
I guess you're talking about a little bit more organisation - today, muck around with racquets and shuttlecocks, tomorrow muck around with calligraphy brushes and ink.
I always remember once in unstructured art time (1980s, substitute teacher...) around the age of 11-12, we were all nailing together strips of masonite, making cross-shaped projectiles about 500mm across, and then flinging them around the oval. They would've been absolutely deadly if that wasn't shut down!
For the rest of us - particularly for dual income parents with teenagers who no longer really "play" - there are organized after school activities.
Its really about odds. You won't get outlier results like Bill Gates or <insert other famous person> but on the flip side you won't get a teenager you have to bail out of jail or a teenager pranking people for Tiktok views. You'll get a decent young adult that can earn a decent living and live independently and confidently.
Play for the sake of playing toxic social media social games?
That way there is not a lot of dwell time to be depressed about missing out on stuff.
Also taking away privileges due to not passing grades, not keeping up with math tutoring, etc. is a great way to get them out of the social media loop.
It gives them a highly plausible and relatable reason to not be active on these platforms (i.e. uggh, I "wish" I could have seen that instagram post but my parents are soo strict!).
Having a big important swim meet or soccer game early Saturday morning is a great reason for not being at Friday's drinking party.