I did that as well, and it was Great and Good and obviously the Right Thing — right up until I pasted in a some shell code which used `` instead of $(). Never again.
These days I use C-z for tmux. It works, and C-z z is easy enough to type when I want to put something in the background.
I'm a committed (interpret that as you like) tcsh user, so yeah, that keybinding gets in the way. On the flip side, it's gotten me out of the habit of blindly copying/pasting shell code, which is a security win, right? ;)
I just switched from C-z to C-q and couldn't be happier. C-z was fine, but I realized it was a really unergonomic stretch. With caps lock as ctrl, C-q is only a slight movement of my ring finger.
These days I use C-z for tmux. It works, and C-z z is easy enough to type when I want to put something in the background.