I don't really understand why sites don't use language headers which obviously specify the user's preference.

Accept-Language headers aren't obviously the user's preference, though. There's the four users that manually set it, and for them it is their preference. Mostly everyone else is getting a default based on their OS language, which often isn't really something they set either.

There's also the problem where the country appropriate website for where you are may not have a language you understand.