So, we used to allow selling deer meat. It resulted in people almost hunting deer in north America to extinction.
The ban is about animal conservation, not food safety.

Your second paragraph already happened, and we’re living in the long tail maintenance cycle that follows.

The current system of deer hunting essentially sets a quota for how many can be killed, and there’s essentially never a problem hitting that number.
In the majority of cases the deer is processed, typically by a certified processor to ensure food safety and reporting of any observed disease, and consumed.
If you don’t want the meat, some processors will process it for you and donate it and give you a discount on the trophy parts. At the least there’s a process for getting donations to people.

I’ve never heard of someone wasting the meat. Not for any moral reasons specifically, although there are those, but just based on appreciation for seasonal treat. It’s getting to the season where I’ll probably be gifted 5-10 pounds of venison, so I’m looking forward to it.