Curators want people to actually visit their museums/galleries in person to see artworks, so they can donate a few bucks at the door and maybe become members. They're not so interested in people who prefer to view artworks in little image files on a computer...
As for making it easier to determine who the actual owner of a particular artwork is, I suspect there are differing opinions in the art world about that. For example, if a painting has been stolen, then presumably the rightful owner(s) would want people to know they were the rightful owner(s), not whoever happens to be selling the painting. But if the painting hasn't been stolen, and is on loan or on a tour of some sort, that could just cause some confusion, and possibly increase the risk of theft. Hard to say, actually.
Anyway, these institutions are hurting, just like publishers are (though not as much). They want people to get out more, not less, and they want people to understand that maintaining and preserving (not to mention insuring and transporting) fine art is not cheap. For many of them, I suspect, this person basically wants to twist the knife.