Why would an attacker give up? The site may stay online but you are still having to pay thousands of dollars+ in bandwidth costs. It seems like a win-win for the attacker.

Because they can't see a site paying thousands of dollars, and they can see a site going down, and they're going to invest their attention in things they can see.

If they were thinking rationally about what they were doing, they'd (a) be demanding money to let up, and (b) breezing right past DNS-based defenses like this.

The attacker has limited resources too, if only because they could be attacking other hosts that drop more easily.