Schools do have that policy, but in my years in school and indeed adult life since then I've never been aware of knowing anyone with a peanut allergy (anecdote not data etc.)
My wife's an infant teacher (5-6yo), and I'm a governor of my son's school (they take 4-11yo). There are about 200 students in each. And there is at least one severe nut allergy in each (i.e. epi pen level), and in both my wife's class and my son's class there is one more minor nut allergy (rash level).