If Uber isn't a taxi service, then could I TM a taxi service named Uber?

Probably not. I mean, you could, but you'd very likely have a lawsuit. Here is the Uber trademark application:

http://tmsearch.uspto.gov/bin/showfield?f=doc&state=4802:tal...

Note the broad claims under 'transport of persons and goods.'

You'd have to consult a specialist lawyer to get a real answer, but it would be risky at least.

Yes, a trademark is a kind of monopoly, on things being named in certain ways. But they aren't monopolies on products or services.