Get rid of the filthy things, rotting carcasses is the big worry. In terms of the balance of native fish stocks, the eco system will re-balance, nature always finds a way. Spotted carp(trout) should be eradicated as well........(that will get a few going )
I couldn't disagree more about them putting up a good fight, I've caught hundreds of the things on both bait and sight casting with lures. You can knock over 6-8 kg carp on 8lb braid and a 3-5 kg stick in no time, after 1 or 2 short runs it's like hauling in a wet blanket.
I think the simple fact is that we all need to live with the idea that the cat is out of the bag, they are here and unlikely to ever be successfully removed unfortunately........