Some banks will sometimes pay more in rewards than they collect in interchange and they must make up the difference in fees and cross-subsidies, but I don't think they'll pay out nearly as much as they do now (lots of 2% on everything options, you can get more if you jump through hoops and didn't miss out on grandfathered cards)
With the EU limit of 0.3% on personal credit card interchange, I don't think they get much in the way of rewards cards; although I've heard business credit cards don't have limited interchange, so there's some larger rewards available if you can swing a business card.
If you're paying interest on a credit card, you're using it wrong, and the rest of us shouldn't have to give up our rewards to shield you from the consequences of your poor decisions.