I wouldn't expect to see any of them in a museum within the next 300 years.
Saw miniatures from several companies in a local museum a couple of years ago. Not a standing collection, though, so they don't quite count. But there's a games museum being founded in Finland, and they're collecting stuff that only 10-40 years old. It won't be long until they or a like-minded institution gets some classic minis for their standing collection.
There's the Miniatur Wunderland (Miniature Wondeland) in Hamburg, with vast railway and landscape dioramas. It's a standing museum collection and they charge for entry. So I guess that counts as a museum for plastic figures, although it's not Warhammer.
The Perry brothers & a hired company produced a massive Agincourt diorama for an English museum, and another massive Gallipoli diorama for an Australian (?) museum. There are your gorgeously painted wargame miniatures in a museum. Yes, it's meant as a display. But I'd bet many visitors marvel at individual figures and appreciate them as well-painted Perry miniatures.
And what else are the Foundry and GW display cabinets than private museums? Already Oldhammerists gather annually at the Foundry estate to drool over old, OOP and some uniquely rare 80's minis gorgeously painted by the founding masters of the hobby. I don't think they charge for entry, but that time will surely come within a decade or two. GW of course charges for entry, but I don't know if they display the older miniatures.
The nostalgia of the 30-60 years old wargamers and collectors is there. It's pure market calculation as to how and where a museum pays for its founding and upkeep. I think it will happen in England or Germany first.
-Z