It's a form of visual entertainment no different from visiting the cinema or a theatre; of course one is to pay for it.
They make expenses housing these paintings just as a cinema does, and have the right to charge to recuperate this.
In fact, I see no reason why musea should even be allowed to be non-profit. — is a cinema ever non profit?
There seems to be a rather arbitrary mentality that some entertainment should be free, in particular whatever entertainment “the cultural establishment” has arbitrarily declared to be “intellectual”, often for no other reason than that it's old.
Wishing to see a famous painting with one's own eyes is no different from wanting to see a famous singer perform live. — a man should pay for it if he wish to do so.