Are we asking the wrong questions about these libraries?

Yes, there will be a few fortunate individuals who can visit them wherever they wind up, especially if they're stored and shelved conveniently. However, many other potential readers will want to access them electronically, over the 'net. That desire on the part of many readers is part of the reason that it's hard to find a home for these books -- or for any books.

Maybe some better questions are these (temporarily ignoring questions of copyright and intellectual property):

How much would it cost to digitize such a collection (or at least the rarer parts not already available in digital form) and then store the books safely but inaccessibly, the way many libraries already have off-site storage for infrequently-borrowed books, while the digital copies are kept online? There would be both start-up costs and continuing maintenance costs (including website hosting) to be considered.

How does the cost of such a project compare to the cost of doing it the old-fashioned way, that is, by putting books on shelves?

Is there a library willing to organize the work and provide the off-site storage if those costs are met from outside?

Is the cost low enough that the prospect of having such a library online would entice the folk community to crowdfund it? If not, would crowdfunding a meaningful fraction of the cost convince some kind of foundation or similar entity to fund the rest?