We let them do running games; we tolerate play fighting, but try to keep to only the children who want to be involved; they are allowed to climb trees and have big outdoor toys and balls at lunch.
We build in movement breaks for all and sensory circuits for anyone who needs them. At times, we teach the curriculum physically eg. Maths, for those that struggle to sit.
We run forest school for all, and have a compulsory outdoor learning part of our school planning seperate to this. It is an SLT requirement to have local playground trips frequently. We have rambunctious free play wherever possible including in EYFS.
We are a trauma informed school and we have MH workers in school for our most affected. All our sanctions are designed with this in mind. We are frequently heavily, heavily praised for our support and inclusivity.
None of this stops the fact that the kids are just pure feral. I am sick of being sworn at, barged, stamped on, hit/kicked; stopping what I'm doing to protect a different staff member; dealing with a playground scuffle that turned into a massive black eye and a nose bleed because both sides got angry and were taught to seriously fight (not play fight), so someone kicked the other at full force in the face... We are not failing boisterous kids (because ours like this are JUST as likely to be girls!). Our school is actually not very nice if you're NOT boisterous because we expect it to be so and it's set up to accommodate it more than for calm and peaceful children. This is still what it looks like. Schools that are set up just how you want them, still have the same problems OP... I suspect we just have rather higher levels of staff assault.