The way I've seen it explained was that the carp had been introduced into the fish farms to check/control growth of algae.
Carp is a delicacy in Eastern Europe. As others have noted, because carp are bottom feeders there is a dirt taste to the flesh of wild caught carp. To get around this fish farmers take carp and put them in pens that are elevated off of the bottom, basically starving them and flushing them out with fresh water until the dirt taste goes away and you end up with a decent tasting fish. This could have been what was going on at the farm they escaped from.
As I've noted, repeatedly, the Asian carp are not bottom feeders in the same way common (German Brown) carp are.
These Asian carp much prefer to feed on plankton and small bits of vegetation.
Once people get that through their heads, they'll be more likely to try eating some of it.
'Merica could eat it's way part-way out of "the problem".