Taking the life of an animal is a strange thing. Some can do it and not be bothered at all, others could never do it but will eat the meat of an animal culled in unknown (to them) circumstances. Some folk can get all spiritual and wierd, leaving a small offering to the animals' spirit ( a kit kat or something maybe!
) whilst others try to treat the animal with the respect it deserves by using its meat if possible (Disease can scupper that plan) and the role they undertake is one of conservation.
There are many other angles you can look at it from, I shoot for the pot and take what I can or leave for the fox. Can't see why chucking a carcass in the bin will do any good, other than create a breeding ground for a few weeks for the flies. The shooting, IMO, keeps the numbers down and stops the wildfire like spread of mixy and other diseases, also stops the genepool getting too small. Having a good shoot allows you to be picky with your targets, take down the older animals and let the youngsters move on up.
Maybe GR just isn't into shooting deer. I know he has taken hares with an eagle and netted rabbits using dogs and ferrets. He's not a complete wuss!