Why do web browsers feel out of place? When I'm using a web browser, it's almost always either taking up a whole screen or exactly half of one--it may as well be tiled already! So when I switched to XMonad, using browsers still felt very natural.
Perhaps it's just a cosmetic issue? For example, if you're using Chrome, you have to configure it to use system borders--otherwise it just looks wrong. I also set my Firefox up to be much more minimalistic, which looks much better with a tiling WM.