It's illegal pretty much everywhere to leave the carcass of a big game animal that you've killed.
The shows you see where they're packing out just the antlers...
Notice how that hunt takes like 30 minutes, sometimes including the flight time and drive to camp?
Yeah, that's because they don't show you the whole thing. No TV show is leaving the meat in the field and packing out the antlers. If they did, they'd get nailed by the law, and have been.
I only hunt deer but I regularly let small and young walk and shoot the biggest I can find, which is generally not very big but still the biggest I can find.
Because shooting the little ones is too easy. Part of the experience is the challenge. If I went in the woods and shot the first deer I saw every time, it would be boring and over quick. No thrill, no chase, no exertion, no reward.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.