Ebook libraries are local for precisely the reason that you stated -- they're handled by your local library, to which you pay taxes (assuming you're a property owner, anyway, since most libraries are funded through property taxes). Because it costs money for libraries to get ebooks (duh?), that money has to come from somewhere. You're already paying for your local library, which is why you get free access. Going somewhere not local means that you're not paying for that library through your taxes, which means you're probably going to need to pay a sign-up fee. Some larger libraries have done that (and some larger libraries that did that have shut down their non-resident programs ...). But then the problem is you're double-paying. You're paying for your local library, which you may not use if you're strictly an ebook reader (like me), and you're paying for access somewhere else.
Besides, once you get away from the "public library", adminstered locally and funded by local taxes, there's no reason to go to a "library" at all. At that point you've basically started the ebook equivalent of Netflix or Hulu, and you may as well run it as a for-profit business.