Which gets back to the question - why does/should the public support a museum. If we can't see it why are we keeping it? Even with our best preservation things will be destroyed over/with time, some things quicker than others. So if people don't get to see it what is the point of preserving it.
Museum backrooms are filled with things that they can't afford to preserve/restore, and so they are slowly being lost without anyone even able to see them in the mean time. Curators hate this reality, but they have to priorities the important things. I want things they can never preserve anyway sold the highest bidder, at least that way one person can enjoy it, we can use the proceeds to preserve something else. Plus part of the value to a rich person is showing off so there is a better chance someone will see it. (if there is no bigger that proves we don't value it. Even if future society would it won't make it to them anyway so may as well trash it now and stop pretending)