This is an astute point. Deeper water is better, apparently. The only place where river turbines have been tried in the US, at least that I could find, were on the Mississippi River, where demonstration turbines, two of them, went online about nine years ago, at Hastings, MN. 

Other projects, further south, were going through the permitting process soon after.  However, I didn't find anything about them after about 2011.