I think it depends on your family and the school. My kids' elem has the playground on one side, a football field on the second side, a baseball field on the third side, parking on the fourth side. The school facilities are used year round by the community.
If your family is active and would use the fields and playground, it would be a great place to live. Or if you are at work during the day when most of the activities happen, it would be fine because most of the school sports practices end around 5 pm here. If you want peace and quiet during the daytime, it would be a frustrating place to live.
ETA: I agree with those who mention the traffic. At our school, the houses that back the fields/playgrounds have wide buffers with trees in between, so I would think those would be pretty nice most of the time, as long as you don't mind a little daytime noise from kids sports practices. The streets in those neighborhoods don't connect with the school, so they don't get any traffic. However, there is a little conflict ongoing right now with the people on the side of the school with the drop-off lane, because they have trouble getting in and out of their driveways during dropoff and pickup times. For us, that's a 15 min window at ~9:00AM and again ~4:00PM. So if you work a 9-5 job, where you leave at 8:30 and don't get home until 5:30, it still wouldn't be an issue. But I can see that it would be annoying if your departure/arrival times overlapped with pickup/dropoff because of the traffic.
However, I personally spend so much time and energy getting my kids to and from that school for school and other various activities, at this stage of my life, having my house back to the school would be great.