I don't know man?
The issue is that, most of the time, "incredibly dense cities" are not the places where this is hitting the hardest. It's the smaller towns where the impact of hospital rollups hits hardest on the property tax rolls.
Problem is, of course, that if we don't get one of the hospitals in, say, Houston, to put a facility in, say, Nacogdoches, on its books; then that facility may go away entirely. In which case you'd have issues in the market with inequity of access for the very populations who may need that access most. (Elderly and poor.) But if you do allow it, well, you have issues with property tax rises.
So local leaders are put in a position of having to weigh the value of having a hospital or clinic be available locally, against any potential decrease in property tax revenues. Now you hope they get that cost-benefit analysis correct, but there's no guarantee.
But churches? Yeah. Not so much.