Many museum policies about cameras are about safety and not disturbing other visitors. Just as tripods are not allowed, selfie-sticks are increasingly being banned inside museums. There is the possibility of harming the art on display as well as other patrons. Large bags and backpacks are usually banned no matter what is inside. As far as the size of the camera is concerned, the museum staff cannot be expected to know who is intending to make "professional" or commercial shots--which may be prohibited--and who just has a big ol camera. Some artists and institutions do not want their work photographed, and that is generally posted in the exhibition. Before smartphones, museums regularly sold slide pages with their greatest hits. They still sell postcards and posters. There may be the theory that personal photography cuts into those sales. It never ceases to amaze me that people take smartphone photos of all the painting in an exhibit. Just buy the damn book! They probably won't look at those photos again, anyway.
I go to a lot of museums, and I go to museums a lot. I even have a project I'm considering about museum guards. Who knows?
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Louvre, Paris 2007