I would think an ideal business model (from a consumer perspective) would be a monthly or yearly fee (I’d probably be willing to pay up to $20 a month) for unlimited access to hundreds of thousands of books. No need to digitally recreate the “library check out” process that places artificial limitations on digital resources. You pay the fee, you get access. Once you stop renewing your subscription, no more access. Your monthly fee goes to the service to keep it running, and to the publishers of the books you spent the most time reading (or flipped the most pages of, or something).
Unfortunately, just as movie studios are stingy about letting audiences have too many streaming options, I doubt most publishers would be willing to allow such access to large catalogues. And this sort of business won’t work if the size of the catalogue isn’t vast enough to attract audiences. It must compete with physical libraries after all.
For now, the only thing that could pry me away from small stacks of physical paper would be easier access to a vaster selection for a cheaper price.