I'd shoot that deer.....but not because he has "inferior genetics". I'd shoot him for his trophy value, to ME.
I dislike the term "cull buck". As far as I know.....a whitetail's antler potential isn't known until at least his 3rd set of hard antlers. By the time they grow thos, though........he's a trophy in most people's book on age alone. He's mature.
Good luck if you decide to take him, though.