They don't even need to offer more money. Offer $1000 and two free return tickets to anywhere in the US, or miles.

I find it hard to believe no one volunteered, even for a small amount, unless they were already delayed

When they do this, it's usually a shittier offer than it sounds. They're not offering cash, but value in tickets, which has an expiration a short time in the future, and can only be applied to certain flights.

It'd be interesting to see statistics on how often these offers are even redeemed.

The few times I've taken the offer, the tickets were good for a year. But for someone who doesn't fly a lot, that is a relatively short amount of time.