I agree with the original poster that this comes off as my way of consuming art is better than yours, whining. I've traveled to over 50 countries, went to the top museums in most of them, walked endless gallery halls, gazed for hours, sat on benches and contemplated, etc. as much as anyone. I've also taken pictures all along the way of things that I liked. Usually with museum permission, sometimes without. I have however, never used flash.(it's a helluva lot easier today with low noise high ISO, and silent shutter mode in the 5d3 is legit).
If I were writing this essay I would be bemoaning museums that don't allow me to take a photo. Yes I can maybe in the gift shop buy an overpriced print and then have it destroyed in my luggage by some overzealous security thug. Maybe if I write the name down I can find the work online and purchase it, but I don't really want it in that form. What I'd like is when I think back of a travel destination, to be able to click a few buttons on my computer to that particular days photos and pull up my photo of it. This evokes much better memories for me, and that's largely why I take photos, to help me remember the amazing things I've seen around the world. Often I can look at a photo of a painting and not just remember details in the photo I had forgotten, but details of the museum and beyond. Maybe where I had lunch, the hotel I was staying at, what the weather was like, etc., all from one photo of a painting. On the other hand if I take a picture of the Orsay outside, I may recall in general that the Van Gogh's are up there, and this part had this, but I really won't recall any detail of any photos. For instance the last time I was in the Orsay the only no-photo area was for some pastels, and they were kept in a dimly lit room. I remember almost nothing from that other than what I just wrote.
The Mona Lisa is a special case. It's a cultural icon. It's like getting your picture in front of the Eiffel Tower. Sad maybe, but that's how it is. Other than that one painting I've never had too much trouble admiring other works in the Louvre. Yes you have to dodge in between tour groups especially on busy days, but that's life in any tourist location.
To me, the greater loss that is happening is I can't be a tourist and record my travels with my camera, thanks largely to idiots that don't know how to work their equipment. It start with a ban of flash, which as others have shown, is not the open and shut case some say it is. With the flash ban you have people that don't know how to use their cameras still blasting away with flash. Finally the museum just says to hell with it, no photos. Then people still take photos and the museum has to hassle with trying to have security hassle people, and this leaves a bad taste for everyone. One of the most preposterous to me is Michelangelo's statue of David. No photo's allowed. They explained it many years ago as some company had paid for the restoration and had the image rights because of this. They have a surly "guard" posted to stop you, or at least they did the last time I went in 2006. Still I took my photos. The guard couldn't be everywhere at once so as soon as she walked to one side, everyone on the other took photos and vice versa. It's stone, even if I was using flash, which I wasn't, my photons wouldn't hurt it. It's one of the most remarkable things on earth(well top 1,000 for me maybe) but I'm not allowed a photo of it. Yes there's a good copy outside where it used to be, but it's not the same for me. This statue survived for centuries outside with pigeons doing their business on it, even a wayward couch tossed from a window taking off an arm, but now, you are not allowed to take it's picture. Insanity.
There's also a growing trend among smaller, 2nd or 3rd tier museums to not allow photography. Just in general, this is often the case because they really don't have much to offer, and when the photos wind up on a Trip Advisor type site business drops off. I personally often don't go to places that don't allow photography. There has to be something pretty damn amazing and one of a kind to get me in that kind of place.
On the other hand, the onslaught of camera equipped cell phones has meant some places have given up trying to ban photography. Thankfully.
Solutions? I've often wondered why most major museums, historical sites, etc. don't have a weekly photographer friendly outside normal hours tour. No flash if you like, but allow tripods. Keep the group together so you don't have to have full museum security staff on duty, 15 minutes in this galley, then so long here, etc., and why not also do the same for those that would like to see the work in a bit more privacy. A special tour, costs a little extra, but you have the museum to yourself, or nearly to yourself.