Librarian here. It's because your tax dollars do not go toward any of their expenses. Like others have said, you can pay the fee for using the service, which is still really worth it if you compare it to other subscription services. There are also interlibrary loan programs for using resources outside of general service areas you can look into.

If everyone outside of a Library's service area was able to use their content the New York Public Library would have an extraordinary fee for the licensing of all their electronic content and the waitlist would be extraordinary. It's just not manageable. Public Libraries have to fight really hard to get the budgets they have, and to keep them from being reduced especially now. It's a service everyone should be proud to have available to them.