> other times that's exploitable, so you just burn the money instead

I definitely see reasons to not pay a counterparty; a swear jar is a one-sided incentive to not swear, where paying the other people present would reward them for tricking you into swearing.

The usual solution to this sort of issue is just donating the money, though. (For instance, productivity apps that hold money in escrow and donate it if you fail to complete tasks.) Is "donating to charity with Ethereum bonds" just too obscure to bother with at the moment, or is there a structural reason the bonds need to specifically be burned?

Donating to a particular charity address is definitely a possibility. The tradeoff is that you're requiring users to trust the people running that charity, if there's an exploit that's damaging enough to be a concern. People also figure that by reducing the supply of ETH you're increasing increasing its price, so it's more of a global compensation to ETH holders than a net loss.

However, charitable donations aren't unknown. The ENS name registry, for example, is planning to require annual rents like DNS, and contribute the money to public goods (e.g. with grants to projects improving the ecosystem).