G&ouml;del&#8217;s proof has the nice feature that one can cleanly separate the logical core of the argument (which is uncontroversial&mdash;but see the next paragraph) from its alleged application to theology (which of course is going to be controversial).  My opinion is that the main significance of G&ouml;del&#8217;s proof is that it shows that there is <i>something</i> to the ontological argument; many people (including my teenage self), when first encountering the ontological argument, perceive it to be total nonsense.  Immanuel Kant&#8217;s &#8220;existence is not a predicate&#8221; objection was taken by many to be a decisive refutation.  So showing that the ontological argument isn&#8217;t completely free of content is already a significant intellectual achievement.

The work of Benzm&uuml;ller (and Paleo) is interesting because it exposed a (fixable) mistake in G&ouml;del&#8217;s proof.  See <a href="https://www.ijcai.org/Proceedings/16/Papers/137.pdf">The Inconsistency in G&ouml;del&#8217;s Ontological Argument: A Success Story for AI in Metaphysics</a> for more details.