I personally didn’t have any trouble getting housing I wanted, but I also had a pretty good lottery number (I’m pretty sure my assigned time was the second slot on the first day freshmen could choose housing). The best way to ensure your son gets housing he wants is to encourage him to select an area he would like to live in, instead of necessarily a building.
For example, my major is primarily based in Park, so I knew I wanted to be near Park so I wouldn’t have to be outside for an excessively long time while walking to class in the winter. When my roommate and I talked about where we wanted to live, we decided on trying for lower quads instead of any particular dorm building. Since there are like 5 buildings in the lower quads, we had a much better chance of getting the housing we wanted than if we had set our hearts on a specific building.
Also, for what its worth, I had a ton of friends with high lottery number that didn’t necessarily get into the buildings/areas they wanted to be in that absolutely love the buildings they ended up in.