I tend to have most windows fullscreen as well. As others have mentioned it is handy when you want to read along side working to have two windows side by side, and this is easily accomplished with tiling.

The big thing that brought me on to tiling WMs is the keyboard driven element.
*Edit - and the minimalism

With regards to the argument about manipulating the windows to suit your needs, this comes with time. Each WM is slightly different but with a bit of perseverance it becomes easier. It took me a while to get use to herbstluftwm after awesome for example.

I also organise my workspaces so that I know which one to switch to in order to find a window. Does anybody else do something similar?