"Master password"'s advantage is the connection to the term, from the normal, non-computer world, "master key".

Sure, but I'm willing to bet that next to nobody who doesn't work with encryption makes that analogy. You also don't typically use a "master key" to unlock a locked box of keys so it's not really a great analogy anyway.

Yeah, I'm aware it's not a perfect analogy, but it's still the best you're going to get for communicating the idea succinctly (just with the name, even) to a lay-person. Alternatives like "vault password" or "locker password" (or something along those lines), provided it's made very clear to the user, repeatedly and persistently, that their passwords are in something you're calling a vault or a locker, can be about as good. "Primary", or anything similar, is worse.