and a software keylogger requires direct access to the keyboard driver, which requires administrator privileges on any sane operating system
No it doesn't.
To access the actual keyboard, maybe. But you only want the key events for a key logger; and that certainly doesn't need admin access. If it did then how would what you were typing ever make it to the application?
Have you ever seen virtual keyboard apps? Or accessibility helpers? Both of those get at the keyboard without any difficulty.