Obviously, with the anxiety issues you mentioned, if you and your son both feel sure that a single room is the best option you should try to get one. I don't know how hard it is for a freshman to get a room in Buchanan, but I do know a few who got in. And it's not like living in a single room means you're all alone and never meet anyone. My entire main group of friends are people from Buch who I met while living in a single room.
But, like other posters have mentioned, a good argument can be made for having a roommate during freshman year. If your son has a friend who is also going to ISU and would feel comfortable rooming with, I'd say that's your best option. And even just randomly assigned roommates aren't the end of the world.
My freshman year, my roommate and I had totally opposite personalities. He was outgoing and liked to go out partying and drinking on the weekends, whereas I'm quieter and more reserved, and not so into drinking. But we found some things we had in common, became friends, and I ended up really enjoying living with him. Sophomore year, I roomed with somebody different who was much more similar to me personality-wise. And I hated it. It wasn't that we didn't get along, but we were just too similar (if that makes sense?). I ended up resenting the guy by the end of the year.
The same thing isn't always right for everyone. I think having a roommate freshman year and then moving to a single later was the right choice for me, but maybe your son would be better off doing it right away. You know the situation better than anybody on here does. Regardless of where he ends up living, I hope he enjoys his time at ISU!