Do any of these extortionists have a reputation for actually stopping the attack once they get paid? I certainly wouldn't trust some random group that's currently DDOSing me enough to pay them.
The rich and weak Frank empire, a bad combination, resorted to the disastrous policy of bribing the invaders to leave. It only served to mark the Franks as a good target and emptying the treasury. The Vikings would leave, plunder some other place and come back for more.
In the end, the Franks ended up giving part of their land on the coast : Normandy. This served to settle the invaders down while making THEM have to protect their newly acquired territory against other vikings.
Your logic is sound - why trust a criminal?
But it's not like there's a better business bureau from organized crime.
Especially depending on the sum of money demanded, I can imagine it being cheaper to either spin up more servers to handle the load, or hire a DDoS specialist to help you out, or make it someone else's problem by moving behind a thirdparty CDN.