I see that there's already an excellent answer framed in linguistic analysis, so I'll come at this interesting question from another direction.
If we grab an online definition of make (from MW)
to cause to happen to or be experienced by someone
and another definition of be (from OD
Used to indicate something due to happen... to express obligation or necessity... to express possibility
we can begin to see the make...be combination as a kind of intensifier, implying an imperative/coercive/causative situation.
Furthermore, if we cling to the sense of make as a near synonym with cause, we might imagine a make...be sentence such as
With a wave of his wand, he made the children be quiet.
as a sort of ellipsis of the infinitive particle to - as if to say he made the children to be quiet.
Of course this does little to explain why "make" and "be" dance this particular grammatical gavotte, other than to demonstrate that, as the man said, "be" is the equivalent of duct tape and WD40 in the English language's toolbox.