The meat isn't very good.
That just depends. Many years ago when I lived in town, I too was on a list and dated one of the local LE dispatchers of a suburban area. During the start of the first pre-rut throughout post rut, with a deer, over-populated park in the vicinity, I got a call on average every other night. She worked night and would call me ASAP as she knew I didn't want a deer that laid very long.
Needless to say, my freezers stayed full as well as everyone I knew that wanted deer. Had to keep my knives sharp.
I didn't have to take the deer if it was badly torn up. Many would still be alive, some not. I'd dispatch those alive and inspect the bodies to see what was broken up. Some would have their necks broken and the rest of the body untouched. So you could make use of most of the meat. Many would have one side beat up which would translate into taking the meat from the other side. One thing I did notice, I could usually get both backstraps.
If the bodies were really torn up externally or badly broken up inside to the point I didn't feel I could make use of much decent meat, I'd just deny getting the deer. Too, knowing most of the deputies, they would inspect the deer and usually knew whether I'd would want it or not.
Too, I wouldn't take any deer during the summer months. Just Fall through Spring. But always had plenty of venison all year long.