What you raise is a valid concern, but letting websites decide on enabling/disabling auto-complete is solving it entirely wrong way around.

If local admin is incapable of configuring user accounts, how are websites supposed to figure out who is who, and which browser is on shared computer?

After all, if managing user accounts is too hard for said admin (or we are talking about a shared PC in a library, which doesn't have user accounts as a matter of principle) - just make browser always start in private/incognito mode on shared computer. It is as easy as adding command-line argument "--private-window" for firefox or "--temp-profile" for chrome. That's it. Window closed - autocomplete gone. Problem solved.