And exactly the same applies to kings or oligarchs. They ought to be virtuous. Few have ever been so. But that doesn't mean that they cannot ever be.
There's nothing intrinsically incompatible between Catholicism and a democratic society. (We're using the term here, of course, meaning representative republic, I hope--I'm sure that's how Neuhaus was using it.) It would be better to use the term republic. But even a democracy could be the servant of society if its members were honest, just, virtuous. If they aren't, all bets are off.
It's just harder to accomplish a virtuous demos than virtuous representives in a republic and that makes a representative republic superior to a true demo-cracy. But Neuhaus wasn't referring to strict democracy anyway.
Granted, the American experiment in republican virtue did not last. But I would caution you very strongly against assuming that the record of kings or oligarchies or noble republics (the old Polish commonwealth of the 1600s, for example) is any better--more kings have been non-virtuous than virtuous, and that includes Catholic kings. And the record of oligarchies is, well, worse. Perhaps the noble constitutional republic would be best but it's been tried extremely rarely in history and the American republic was the closest to it in many ways. I'd beware of nostalgia for feudal kingship.
The quote from Neuhaus, as far as I can see, accords fully with JPII on culture being prior to the state and the state being the servant of culture. I really don't see the problem. It's not naive, assuming that he's giving a prescription of how things ought to be. He's not saying that this in fact is the way things are, is he? You've pulled this out of context.