Some people's ideas about state schools are very odd! Maybe the ones where you live are bad but in my area they are mainly rated outstanding/good and don't have a reputation for being plagued with problems.
To answer your question I started to let my DS have some independence outside from year 6 of primary but that was initially just to walk to the local shops and back or to walk to school and back on tie or own or with a friend.
It was done gradually and with lots of rules in place.
At 12/13 I relaxed a little bit but still the following applied.
Can I go and hang out at the park? - no
Can I go to the park with X and be back in an hour? - yes.
Can I go to the high at and hang around - no
Can I go to the high at to get a specific item/ have a coffee with X at Costa and then come straight back - yes
Now at 14 I'm happy for him to come as go as long as I know where he is going and who he will be with. I never allow him to just hang around - he has to have a purpose.
He knows who the kids are who he should avoid associating with. He knows to come home if he sees trouble brewing. He knows the places to avoid.
DD has just turned 12 and she is now able to meet a friend for coffee or go to the shops or park as long as we agree times and I know at all times where she is. She also checks in every now and again to let me know what she's doing.
Obviously the pandemic has put further restrictions on their freedom but they've still managed to have socially distanced meet ups with friends.