...why do they always seem to concentrate their fire on churches and cathedrals and places of worship?
Surely one of the most important reasons the Church needs to have a revenue (apart from to perform its charitable works) is that it requires an educational and intellectual infrastructure. I have been reading profiles of Cardinals who are considered papabile (which, as you know, means "a possible candidate for Pope"), and I am struck by how much education and training and administrative experience is required of a Cardinal. And of course it would be.
The superficially romantic view of a Church that is formed entirely of mendicant monks and worker-priests would be, in fact, an intellectually and culturally and (ultimately) a spiritually impoverished institution. Christ's kingdom is not of this world, and yet the Church must be (in a certain sense) a world of its own. It needs a body as well as a soul. It needs brick-and-mortar spaces where it can pursue theological research, train priests, formulate social and cultural policies, and so forth. Otherwise it would have no independence of thought-- it might cleave to its dogmas, but would it be able to defend them?
The pilgrim Church may never have "where to lay its head" in this world, but it needs at least somewhere to stand if it is going to move the world.
It may be an obvious point, but it hadn't occurred to me until this evening.