BE is different from other verbs.
Morphologically, it has extra inflections which other verbs lost centuries ago—1st person am and was, and an infinitive (be) distinct from the 'plain' (present) form are.
Semantically, it is virtually meaningless: in most of its uses it does nothing but convert an attribution into an assertion (the good man → the man is good).
And syntactically it behaves like an auxiliary even when it is the only verb in a clause: it inverts with the subject in questions, it 'codes' its predicate in tag questions, and it sustains negation and emphasis, all without do support.
The contrast to another common verb with both 'lexical' and 'auxiliary' uses is instructive. Until quite recently HAVE might also behave like an auxiliary when used as a lexical verb, but these uses are disappearing in present-day English. Today the auxiliary and lexical functions of HAVE are almost always distinguished:
NEGATION: You aren't happy. You haven't finished.
but You don't have a car.
INVERSION: Are you happy? Have you finished?
but Do you have a car?
CODE: You're happy, aren't you? You've finished, haven't you?
but You have a car, don't you?
EMPHASIS: You ARE happy! You HAVE finished!
but You DO have a car!
In light of this contrast, contemporary linguists tend to classify BE as an auxiliary in all uses, not just in passive and progressive constructions.