A lot of people are under the mistaken impression that the Catholic Church has vast piles of money sitting around in a Scrooge McDuck-style money bin. Whereas if you look at the balance sheets of your average Catholic parish or diocese, you'll see that their budgets are relatively modest, they sometimes operate in the red, and to the extent that they have liquid assets, they're generally set aside to fulfill pension obligations.
Even at the Vatican level, the annual operating budget is roughly equivalent to a mid-sized U.S. city, and expenses tend to be fairly close to income. The art in its museums is often mistakenly viewed as if it could be sold off like gold or diamonds, but the Vatican actually acts more as a conservator than an owner of the pieces. It does not consider itself at liberty to sell the art, because it was entrusted to the Vatican's care under the expectation that it would be perpetually maintained. In that sense, the art truly is priceless; it can't be sold.