But libraries already have floating e-book licenses you can check out for downloadable content (including off hours) in addition to everything else they offer.
My daughter volunteered at the local library this summer teaching younger kids to read. In theory some semblance of this "could" be done over the Internet, but I just don't see it actually happening, and it wouldn't be the same.
Just so. In fact, these days it seems like libraries are more about being community centers than a place to borrow books. Where I live now it's not quite as noticeable, but in my previous city there was always a line to get on the computers, but hardly anybody browsing the stacks.
My library hosts story time for kids, book/movie/anime clubs, beginner PC classes (typing, office software), board game nights, arts and crafts for kids, arts and crafts for adults...all free. During tax time, they have all the forms and information you might need, and they provide information sessions and classes on free e-filing. They also host paid events; recently they had a LEGO exhibit with competitions for kids and open build time, and a Tor editor and author Q&A session where they critiqued the first couple pages of attendees' stories. Granted these things could be hosted elsewhere, but being at the library makes it more likely that I'll hear about it and far more likely that I'll go.
Also, my library also gives me access to subscription sites, including ebook and audiobook sites. I can pay $100 per year to subscribe to ancestry.com, or I could go to my library. I can pay $260 to get lifetime access to a single language on RocketLanguages, or I could go to my library and get access to every course on every language they have for free. While the interface isn't as slick as Duolingo, there are more languages available and it just feels like a better way for me to learn.
And of course there are the books themselves. My city has a pretty solid collection of sci-fi/fantasy, though it's not quite as exhaustive as my previous city. One nice thing they do here is try to have plenty of copies of the first books in a series, something that was a big annoyance before. I can't remember how many times I saw an interesting book while browsing, only to find out it is a sequel and I'd have to request the first one. I could also check out e-readers themselves, something that is relatively new both here and my last city.
TL;DR: you might replace one single aspect of libraries with something like Kindle Unlimited (and poorly at that), but that's not all libraries provide. Not by a long shot.