I always thought the norm of first-person UF arose from the old standard of private-eye stories told in first-person. Part of the entertainment is to absorb the main character's wry and usually jaded point of view as you escape into their (usually) unenviable world. The immediacy of their p.o.v. lends it a sort of authenticity that third-person would have to work harder to lay out for you without a fantasy-world setting.
Now, maybe a disproportionate amount of UF may be compared easily to gritty private eye stories on some level -- i.e. plenty of UF is literally private eye material with fantasy elements added, or placed in a fantasy setting. But I think perhaps even the non-crime/mystery UF stories often face the same challenge of transporting the reader from their familiar world into some sort of underworld, parallel world, or near-future world that's supposed to take place in a hidden part of that same world the reader knows. For me personally, the immediacy of the first-person p.o.v. helps make that transition authentic even though the same story may be told successfully either way.
I'm reading Water for Elephants at the moment, not urban fantasy but escapist enough to occupy the same part of my brain (I got into it because of its elements in common with the fantasy/horror series Carnivale). It's first person and present tense, and despite how I occasionally read criticisms and warnings about that form of writing -- as if it should be avoided lest it create a distraction for the reader that wakes them from the "fictive dream" -- I'm finding it makes the transition to the alien world of Depression-era travelling circuses all the more convincing. Especially since the story flashes back and forth between the present and past, while maintaining the same present tense, sometimes with a passage in common between the two eras to create a dreamlike transition between them.
The OP made me review favorite stories in my mind, and it turns out they're most frequently first-person, making me pretty much useless for recommendations.
If I remember correctly, The Lathe of Heaven by Ursula K. LeGuin was told in third-person omniscient (I remember finding that unusual in itself for this kind of story), and I found that to be a knockout. Some might argue that it is more scifi than urban fantasy, but despite scifi elements it was grounded in the theme of changing the present and near-future of our familiar urban society (or more to the point, recognizing it differently through changes of mind) through the device of a purely fantastic story element.
