OP, this all makes sense to me too.
However, reluctantly, I also have to recognise my DC are different to me. I was / am v academic (my DSs will I hope do fine at school / university but they don’t have that interest I did), I’m a do-er, always going. That’s my way to relax.
Thankfully we are all sporty so we have that in common, but when they are not playing sports, they would do … nothing.
On balance, I think you are right to keep pushing. With my DS, I have insisted on outdoor time before 12 - run, park with friends, GAA club (we’re in Ireland). They moan & complain BUT are better for it & I can live with the screens a bit then. And my youngest is significantly less dysregulated then.
We are parents & have to keep doing what we think is best, taking the chance it will be wrong.
in your case, I might insist on eg an hour’s cooking with you for family dinner but then let him at the gaming for 4 hours (but not longer).