Well, Amethyst can float windows so I wouldn't call it a tiling-only WM, but there's a lot of reasons I prefer it over floating window managers.

I'm really lazy and want software to deal with my windows for me. I used floating window managers for a long time and found that I spent a lot of my time arranging windows in the same patterns.

I also found that with floating window managers were just too limited for things I wanted to do on a daily basis. Two come to mind off hand. I want to be able to make a window temporarily bigger, but keeping the other windows on the screen and sized appropriately and I want to be able to easily switch which window is the "primary window." When I'm doing web development without external screens I find it very help to have an editor and a browser window open at the same time. One of them takes up about 80% of the screen and the other takes up about 20% of the screen, but I switch which is which pretty often. Make the editor take up most of the screen, make some changes loosely referencing things in the browser window, make the browser window take up most of the screen and see effects loosely referencing the code in the editor. And sometimes I've also got a Hulu or Netflix window open taking 20% of the width and 50% of the height. The complexity of making that work with a floating window manager is just too much compared to how easy it is for a tiling window manager.

I also just like being able to see everything on my screen at the same time.