It doesn't help that the Spartans have a history (deserved or not) of being the bad guys because of how we interpreted classical greek history, Athenian texts were just more available.
Even today my civics class teaches of ground breaking athenian democracy, despite the fact that Sparta did it first. Sparta can't get a break.
Well... let's not pretend that Sparta was democratic in any real sense. Yes, they had a "constitution", their government had some democratic elements, its male citizens were considered equal, and women were treated relatively well. But they weren't a democracy, not by any standards - including their own, which, to me, is as important as anything. Spartans would never have considered themselves to be living in a democracy.
That said, your main point is absolutely correct. Sparta has a reputation as being a bunch of, as my political science prof said, "ignorant lunkheads", a reputation which completely derives from our history being Atheno-centric, and really isn't fair to give.