It’s a truism of Protestant biblical hermeneutics that, whatever else you might be able to do with allegories and typologies, you cannot use them to prove doctrine. “Allegories are fine ornaments, but not of proof,” Luther said in The Table Talk of Martin Luther.
Paul never learned this rule.
In the one place where he explicitly indulges in allegory (allegoroumena, Galatians 4;24), he uses it to draw the conclusion that “we are not children of the bondwoman but of the free woman” and to encourage the Galatians to toss out the bondwoman and her son (Galatians 4:30-31).
Exactly how this constitutes any kind of proof is certainly elusive. That Paul argues by allegory is indisputable.