Hence my question: why don't keyboards have a password key which must be pressed before entering a password, so the OS can take an appropriate action?
So, you need an extra step to stop you from getting your password into files like .bash_history and from submitting it inside auto-submit search forms (eg. Google Search or any autofill field).
For the former (or anything that doesn't auto-transmit), don't press enter.
The latter is a newish usecase that I am sure we can fix in a better way (eg. attempting to type any password from your keyring into non-password field could delay that until confirmation is given).
If you wish, you can always write a program that pops a password box on your assigned key, and then emulates keypresses. You'd similarly catch your passwords with a keylogger-like app that integrates with your keyring.
TL;DR — because it's not a big deal, except for some new usecases, and it wouldn't be a great solution.