That’s an incredibly good point. Bad actors are the worst. Some ideas:

• Maybe you’d need to contribute your storage capacity +10% (or more), to account for your and other’s downtime during disasters.
• A time limit after disasters would be necessary. It’s difficult to think of a proper time limit though, as even a month might not be enough time if your entire house burns down.
• Maybe a payment system could be set up to where, if your server doesn’t ping for a week, your credit card is automatically charged (after pinging you with many emails). Sure, that’d suck, but it’d be better than loosing your data, and cheaper overall than paying for cloud backups. I’m not sure where that money would go. Maybe distributed to those who didn’t experience a disaster, or maybe to the software project, though that would mean people are profiting from a disaster. Maybe it could go to a charity of your choice or something.

Definitely a difficult problem to solve.