This society is entirely built around quirks, there's no reason why there wouldn't be spaces or facilities where people can use their quirks if their lives depend on it.
@AxeBurningfire their society isn't built around Quirks, most people don't use their Quirks in their daily lives as most have pretty useless ones. The main series and the prequel spin-off have also shown that their society looks down on people with villainous Quirks, treating them as villains even. So it makes sense the kid would try to handle it himself