It's fairly well known, as far as I can tell, that much of Europe's best physical art (not just paintings but everything available) was looted by the Nazi's and either kept, stored in Switzerland forever, or sketchily brought back into circulation by those willing to quietly buy and store in private collections those pieces with highly questionable provenances. Also, of course, many famous works have independently been stolen never to be seen again.
Just curious what rough % of the world's most incredible art will likely never be seen by public eye vs what is actually in public places ie museums? Would the Louvre even rank in the top 100 collections in the world if compared with private/secret collections?
Cheers all!
The biggest limiting factor, actualy, is display space in the museums. For every painting you see on the walls in large museums like the Louvre, there are dozens in storage. This is one of the reasons why most museums are frequently organizing special exhibitions and temporary galleries: it gives them a chance to show off some of the lesser known objects and art pieces that are languishing in storage. But even so, most pieces will never see daylight, and are only taken out of storage when visiting researchers need to examine them.
You can get a sense of how much amazing stuff is hidden in storage by browsing the British Museum's online catalog - there are millions of objects in storage, but the building only has space to display thousands.
I can't comment on how many masterpieces have been lost to looting and private collectors, but many of the world's lost treasures are waiting to be discovered in museum storehouses, where they've been carefully preserved in the hope that, one day, someone will be interested enough in them to have a look. Often, all you need to see these hidden treasures is a proper research question (and sometimes, but definitely not always, a university affiliation).
I have been trying to think about how to answer your question, and I'm not sure it's really answerable. As /u/alriclofgar says, most museums own many more pieces than they can ever display, and given professional strictures on deaccessioning works, most of these will likely never be sold, except perhaps to other institutions in order to acquire other works.
That said, you are right to highlight the black market in art that came out of the Holocaust, as well as various stolen works. Another huge problem are stolen antiquities, particularly out of places like Syria and Iraq that have seen long-term violence and religious extremism. Further, recently art has become a popular investment commodity, with syndicates buying up works to keep them as investments, locked in vaults, rather than for display. Theoretically, these works might be sold and once again find the light of day, but who can know when? Finally, there is outright destruction, as happened in, for example, Bremen in 1942, when bombing damaged and destroyed works in the museum.
How to express it in a percentage, though? I don't think you can. My instinct is to say that the percentage, over the lifespan of the human race, would be quite high. But of course, if something doesn't survive it by usually (but not always) becomes less important, especially over a timeline of millennia, so you enter into a kind of tautology where only things that survive become "the world's most incredible art."
I know that isn't a terribly satisfying answer, but it's the best I feel I can do.