No, I don't think it is the music per se. I think the reason you see more "postmodernist" stagings (and BTW, the Germans have a great word for this, Regieoper, "director's opera," which leaves the modern/postmodern distinction out of it) is that
(1) a historically accurate 18th century staging would look very strange to contemporary audiences, since almost all our ideas about dramatic "realism" on the operatic stage postdate this period. Remember that opera in the 18th century was staged in very small theaters, with the house lights full on, libretti in everyone's hand, and a full panoply of activities going on in the boxes, etc. Also, people went to operas over and over, so they became more a sequence of things to cheer at or ignore, and less of a "story" you watch end to end. (An opera in this time was more like a baseball game, and much less like a movie.)
(2) There is no tradition of staging these works that would bridge the distance between then and now. The operas of Mozart and Rossini, for example, are just as "dated" in some places, but we have an unbroken tradition of staging them that creates a range within which a director can work without a "concept" seeming to intrude. But with Handel, there is no "normal" way to do it, since the operas did not stay in the repertory.