Honestly do we need more site extensions? I feel like these days most extensions like .com/.net/ etc tend to be for just about any sites these days. Not sure if people would want to write out longer extensions either. So .library probably won't get used. If anything maybe .lib or something would suffice as it's shorter. You kind of want your extension to be short, that's why we have .net, .com, .io, .to, etc. People don't like to have to type out lengthy domains.
That sounds like it'd be too much imo. I think a better alternative is to use the state instead of every city or town. Like this: .CA for California, .TX for Texas, etc. Doubt every profession will get one too, seems impractical to me.