I visited Rome with my family a few weeks ago- what an extraordinary experience for a history enthusiast.
The number and density of churches astonished me- one is rarely out of sight of one, and there's often more than one on the same block, or right across the street from one another.
Many of these, while they must have been expensive to build and they're magnificently decorated, can't accommodate very many worshipers at a time, so presumably they weren't built to accommodate a large community.
Why are there so many? My theory is that they were vanity projects for rich Romans and prestige projects for rich non-Romans.
Many churches in Rome are in some way connected to a religious organization or region/nation outside of Rome. Those would indeed also finance the churches. And remember that because of the way the papacy was assigned, there wasn't just one noble family in charge of Rome, but many different ones had their influence on it, and wanted to show it. The Borgia, Medici, Farnese etc all had to have their power clearly displayed in the city.