If you can send headers with routes then I suppose you could cache with them as well. Although that could also get a bit tricky if you didn't want the routes to enclose an entire document. The typical use cases i'm thinking of would be a json route and an image route.

Probably, all a bare minimum viable url router should do is display some content based on a url or fail to an error code. I would post my own experiments with building a url router that deals with everything (because I tried it) but the end results were objectively worse than what's already been posted here... i've found that it helps to have the router, and whatever process handles rendering the document as a whole (including headers and caching) be completely separate.