Primary teacher here, and parent of two ND DDs who needed a lot of big, physical play when younger (now channelled into sports).
Teacher training includes early childhood development, and the pedagogy of play. EYFS has play -much of it physical- 'baked in'.
Obviously, not every teacher has 'boys in their family', but we don't necessarily expect other professionals to lead from lived experience: fraud investigators don't need to have tax cheats under their own roof, nurses are not required to evidence acute medical need in the ranks of their families in order to practice well.
School is a place where children spend part of their days and as such, it is expected to hold a lot -but not everything. Schools, in my experience, understand the value of play -including physical play- but are in a difficult situation: the health and safety of everyone on the premises must be front and centre, this can't be disputed. Local authorities, and subsequently school leaders, make risk assessments to ensure this remains the case, and schools are audited by local authorities to ensure they remain compliant and have strategies and policies in place to keep everyone safe from harm. This is a baseline which schools can't get away from.
In schools, seemingly small 'incidents' can blow up: parents are, on the whole, understanding of accidents and even minor scuffles, but many are litigious and threaten legal action in a heartbeat: was my child in view of an adult when it happened -if not, why was there not adequate supervision? How come such a fall was possible -why no non-slip surfacing in that part of the playground? And on it goes. Every 'expect to hear from our solicitor' takes up a huge amount of resource in terms of evidence gathering and preparation.
With my DDs, a big part of their childhood consisted of me ensuring they had the opportunities for large-scale play their developing bodies continued to crave, right up until late primary school: visits to the park, the woods, giving over part of our (tiny) home to physical play, school clubs and extracurricular activities, play dates with like-minded DC. But I didn't expect school, in it's day-to-day business of fostering a regulated, calm learning environment to meet the lion's share of my DC's need for physical play. My DC had to read the room.
I do think we start formal education much too young in the UK though, and in an ideal world, children would attend forest school settings -yay!- or similar, until 7. They'd still 'catch up' academically, no question about it. I'm from a country where this is the norm.