Why not raise pigs or chickens, for a simple and more reliable meat source than chasing deer with a car? If hitting a deer is needed to feed a family, then all the people who don't get lucky starve to death.
That is done. If you live in a rural area, hitting a deer is not uncommon. If you take it home to eat it though, you're poaching. A game ranger told us on a class trip one time after a student asked about hitting a deer if you could eat it. He said, "If you hit a deer, call us. We know lots of hungry families, but don't load it up and taking it home. That's illegal."