Pretty serious about it myself montana and here are a couple of thoughts. First check your regs as some states prohibit wasting of taken game or fish. Not sure how it is now but when I was fishing for them in Washington State it was illegal to bow shoot Carp and discard. I will admit I did go after them with a bow a couple times but what challenge is there to shooting a fairly big target from 15 ft or so? So I gave that up. In general if they are taking the fish to eat, and yes they are edible, in fact quite good when canned, bow shooting is ok by me. other than that I view comments such as I use them for dog food, or garden fertilizer with a jaundiced eye?
As for those pursuing them with the UK/Euro Carp rigs and techniques--quite sporting and fascinating to boot.