Sorry, clicked enter too soon; here is the rest of my post:
The ban on lead shot (for hunting deer and other land game) was, as you wrote, based on concerns regarding lead exposure in those who ate shot venison. A study released last week by the North Dakota Department of Health & the Centers for Disease Control (CDC) found that those who ate a lot of wild game tended to have higher blood lead levels than those who did not; more recent wild game consumption correlated with higher blood lead levels.
Even if you argue that the ban on lead shot is unnecessary, the ban is intended to protect those who eat wild game from lead exposure. It’s not an attempt to take away ammunition, since lead-free ammunition is available.