What I don't understand is how both screen and tmux ship with bindings that conflict with readline. Did nobody notice, or did nobody care? Neither is usable without fixing this in config.
Configuring the prefix key to C-z is quite harmless, C-z C-z for suspend is quite ok.
(As a bonus hint, binding subkeys with control it's faster to send commands: C-z C-n is faster than C-z n, you just keep control pressed during the command sequence.)
Of course, it's easy to fix. It just boggles my mind that they would have made that mistake in tmux to begin with when you consider that it's one of the main complaints people have about screen and tmux was supposed to be a "better screen".
How about C-q as an alternative? It is same as C-v (in the default readline mapping) and generally unused. It does not conflict even with Windows' use of C-v.