I think a big part of the problem, with public libaries, is that they've tried very hard to become far more than just the "essential service" that they started out to be.
For example: I think that libaries can fulfill a valid need for providing some entertainment in their communities, but, for libraries that don't already rely solely on donations for books to serve entertainment needs (and I bet some already do), the extent to which many libraries expend public resources to provide such books has resulted in an arguably unnecessary hit on budgets.
But worse, you go into some (though perhaps not your local) public libraries, today, and you almost get the feeling that you're in a Blockbuster, with a vast array of arguably
premium entertainment options. Again (I have to keep reiterating this because otherwise some folks will miss the point

) many libaries already do restrict their expenditures on solely entertainment options/premium entertainment, but the ones that don't, yet,
should, and quickly.
Also, while providing public Internet access is critically important IMHO, the use of public Internet access for
entertainment purposes has substantially reduced the extent to which that costly service serves the public good.
Now I'm very sure that folks can come to the defense of some of the things I've attacked, above, but in reality
that (the fact that so many people choose to come to the defense of those things) is the reason why fees like this get traction. If we cannot come to general agreement bounding the free services of libraries to just some more 1950s version of what would be considered the essentials, then we cannot reasonably expect to get away without big tax increases every year (since the demands for, and costs of, premium services, increase every year), or new fees imposed on everyone (thereby having people who just need essential services subsidizing the non-essential entertainment of others).