Thank you, therefore my first impression seems right: without any provision for UDP this isn't an easy-to-setup and transparent way for any user to preserve his/her privacy.
As always this will depend on your definition for "any user".
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.