Related: I happened to notice in the credits of the movie
Hancock a line about "the image of the Empire State Building was used with permission from ESBC."
After a groan, an eye-roll, and some Googling, I found
this, which initially sounds aimed at professional and/or movie shooting, but the second paragraph sounds universally applicable. I'm sure they wouldn't seek fees from just any hobbyist photographer, but if you happened to make a skyline picture so fabulous that you could sell prints of it for profit at your gallery, and ESBC got wind of that, they might try to collect. Isn't greed (sorry, "monetization of intellectual property") lovely?!
BTW: On the subject of museums, maybe as others have said they are trying to protect exhibits. Maybe copyright owners are "forcing" them to forbid photography. But I suspect greed mostly governs here too: Museums quite happily forbid photography so that if you love an exhibit so much that you want to see it from time to time at home, you must pay their extortionate gift shop prices for books/prints rather than snap a picture for yourself.
--Dave