It’s nice that you acknowledge it.
Sadly, the Catholic Monarch never worked - well, Isabel of Spain was probably about the only one who even came close - even though the idea of a ruler informed by Catholicism is not a bad idea. However, even a “Catholic Monarch” is not a representative of a theocracy, but simply a monarch who subscribes to Catholic principles. Such monarchs are pretty thin on the ground, though, and I don’t think you can build a political theory on their existence.
Louis IX, of St. Louis, Missouri fame, whose feast we celebrated on the 25th springs immediately to mind. Monarchists get all misty eyed about Charles I of Austria as a "modern" example. Actually there's quite a herd of "good" Catholic monarchs pre-reformation but since then certainly they're rather a rare breed.
To me Catholic monarchists are a bit like Star Trek fans... or Civil War reenactors... or sports nuts. As long as they don't show up at the office in uniform they're pretty benign. I'm all in favor of the occasional harmless eccentricity.