Entering Chinese characters requires using an input method engine that turns keyboard input into a list of candidate words from which the user picks the correct one. If you used that method to enter a password, shoulder surfing would be trivial. I think it's usually automatically disabled for password input fields.
Additionally, there are other methods like Zhuyin that some people (typically the older generation that used computers before contextual dropdowns) use. I believe those keys just map 1-1 with American keyboards so they would just type the keycodes for Chinese characters and ASCII is inputted into the password field, but correct me if I'm wrong.
Zhuyin is just another way to input Chinese phonetically, so it requires the same feedback mechanism to choose the correct character. You're probably thinking of Cangjie, which was designed to have a unique code for each character, so theoretically it doesn't require feedback but modern implementations seem to have it anyway.
It's never allowed, part of the reason is you need to install Chinese IME to begin with.