The first issue is you don't know when or why it was killed.
If you pick something off the roadside, maybe it looks fresh, but it only has to have been there a day or so and who knows what has crawled into it to lay eggs, licked it, nibbled at it, etc.
It's possible that the animal was hit by a vehicle because it was already sick and wandered into the road. Not being able to see the way it walks etc means you can't know this.
What is the difference between a bow/gun-shot deer and and a
road-killed deer, in terms of health concerns?
If you shoot or otherwise kill an animal for food purposes, you could be unlucky and it have some disease or parasite etc. However at least you know it was fresh and how it died, and can see it's movement beforehand.
Also a professional hunter will kill it without damaging certain organs and bones. Being hit by a car might mean the animal has burst organs that can taint the meat. Or shattered bones that are distributed in the meat you end up eating.
Personally, I don't think it's worth the risk at all. But many do, and I guess you can become reasonably experienced to identify if it's safe or not, like picking mushrooms and knowing which ones are safe to eat.