alt Hacker NewsArchive is likely one of the top traffic destinations on the internet. Your local library is likely not.
Maybe they want to hire someone full-time is so they don't have to have a policy of whenever they feel like it?
Having a reliable service is likely one of the reasons why their donors donate in the first place. Why do organizations and wealthy people still want to donate if the service goes down for 2 days and no one cares? Why would this kind of non-profit attract top volunteers in the first place?
High traffic doesn't mean high urgency. New York Public Library is huge and looks to have even more restrictive hours than mine. They're closed on Sundays!
People donate because they believe in the mission, and most of the money probably goes to the actual storage (making the cost of an employee probably pointless to care about, of course).
It would attract top volunteers in the first place because they'd think "I want this to exist, and perhaps they need some help." No one's going to think "wow the wayback machine was unavailable for two days? What a bunch of amateurs." Actually even if they paid me $200k, I'd assume they have some priority issues if they wanted me to be on-call and couldn't convince me of why that's necessary. That'd be a huge red flag for some nightmare mismanagement.