I am looking for the most famous object that can be seen in person by an average member of the general public, but has never been photographed (or at least, any photographs of it have been destroyed and future photography is prohibited), such that the only way to see it is to go visit in person.
Is there such a thing in the modern world?
Note that I said “most famous”. That implies it has to be somewhat famous, such that you’d actually want to see it, but photography is prohibited or otherwise impossible.
I’m not sure there are any published photographs of whatever it is that passes for the Ark of the Covenant inside the Church of Our Lady Mary of Zion. But it gets passed off as the actual Ark, so in one sense what’s inside is “famous” even if it’s not the Ark (which, sadly, it probably ain’t).
I have read that its guardians are not disposed to average people gawking at it, so I’m inferring from your OP that “average person” means an average guy could see it if allowed. The dilemma here is permission.
is it required that the object is visible to the general public? If not, then something like the alleged Ark of the Covenant in Ethiopia would probably qualify (has any person other than its caretaker, Orthodox or not, been allowed to see it?)
If so, I’d make a WAG that candidates might be found on military bases. For example, personal photography is forbidden in some sensitive areas in the US that one can visit relatively easily. For example, the outer grounds of the Pentagon may be visited without a pass, but there is a sign that you are subject to search anywhere on the outer grounds (though they don’t seem to actually do that). But then, there are plenty of photographs OF the Pentagon that you can find.
When I was in Xian in 1985, photographing the buried terracotta soldiers was prohibited. One could go inside the structure to look at them, but you’d have your camera confiscated if the guards saw you take a picture.
It doesn’t quite fit the bill as a single object, but sometimes you get viewings of dead celebrities that are open casket and open to the public. Any old schlub can show up and gawk all they like, but they usually have goons on hand to make sure nobody takes any pictures.
Although, along similar lines, Kim Il Sung’s embalmed body might fit the bill. His mausoleum is the biggest tourist attraction in North Korea-- supposedly most North Koreans are expected to visit a few times a year and if you do one of the very-guided tours it’s pretty much a mandatory stop. But it is definitely not a spot you are allowed to take pictures and security is insanely tight, even by North Korean standards. Perhaps there are some official pictures somewhere but, other than some grainy shots from his funeral, they’re not on the internet.