That's a great question. Zsh and tcsh both use stdout for their prompt, ksh and dash use stderr for the prompt itself but stdout for whatever the user is typing into the prompt. Bash, at least as it's configured on my system, seems to use stderr for the prompt and whatever the user types on it.

I really can't think of a reason that the way tcsh and zsh handle this isn't the proper way. Surely the principle of least surprise applies here.