Internet Explorer (of all things) already had the right idea with its "previous IE" mode: if the renderer emits standards errors while parsing the site, offer to retry with an older renderer (and send that renderer' original UA.)
The newest Mobile Safari has a similar idea: if a site seems to force certain mobile viewport constraints, then offer to redo the request with a desktop UA instead of expecting the site to know how to set a sticky-session parameter of "desktopness."
In fact, Chrome's "Translate this Page" popdown might be the best example: you get a page you might not understand, along with an offer to magically fix the issue (which is nevertheless optional, because the user might speak that language after all.)
To wit: let old UA-detecting websites break. And then notice that they did, and offer to send a "compatibility UA" only in those cases. Turn a cost browsers were eating into a light punishment (but not impairment!) of the websites responsible. A carbon tax on archaic coal-powered websites, in a sense.
(And note that this wouldn't have to be work repeated by every user, or even seen by many at all. Google could build a perfect pre-seed database for this just by doing comparative search indexing using Googlebots that send differing UAs.)