Why would they crack something that can be played for free?
People who enjoy "sticking it to the man" are prepared to run Linux as a desktop OS. So they're no strangers to suffering pain for no tangible benefit beyond being a rebel.
If the crackers can't find the motivation from being heroes of the underground to being a rebel, then the paying customers are certainly not going to find the motivation to stump up cold hard cash for a game they can already play with ads.
So you end up just going back to a revenue model where everyone gets ads and there is no registered version. Probably work better that way. No DRM, integrate the ads fully into the game.