Many decades ago, we used to have chat scripts for dial-up logins. These scripts were sometimes intricate, designed to get past the many nonstandard prompts that sysadmins generated before you could log in. Eventually PAP or Password Authentication Protocol (see RFC 1334) was implemented which made such logins a lot easier.
I think we are at that point now. Some password manager implementer needs to propose a standard HTML fragment that will include the usual login fields and that can be correctly recognized and filled in by every password manager. The standard should be simple enough that even the most clueless website designers can implement it.