Non-TCP activity wouldn't route and will fail to send.
Maybe I'm wrong, but it seems similar to I2P where if you want "UDP", you'd need bespoke plugins/transports/whatever for each application.
Users who try to do a lot of UDP traffic will have to change their habits, yes. But a majority of users who don't know a lot about computers rarely do anything on a PC that isn't driven by the browser anyway.
But at least the users who try to use UDP won't wind up specifically leaking info, just wind up slightly confused why certain things aren't working.