the point of view of neighbors who complain about the noise of a nearby schoolyard? We keep getting notices that the neighbors of our school building are upset about the noise. I can imagine if you have a baby or a night job it might be frustrating (much like sirens or NYC nightlife) but kids playing outside between 9 am and 3 pm doesn't seem like something to complain about to me. What am I missing?

No idea. One would think that the schoolyard was there before the neighbors moved in. Did they not know that children playing in a schoolyard make noise during the day? Weird.
Some people don't know the difference between something that is their problem and something that is someone else's problem. They probably used to work in an office during the day and now that they're working from home, the daytime noise is distracting. Fine. But this is THEIR problem to solve. Headphones, white noise machine, window shutters. Not the school's problem.