Any time you place additional requirements on an actiivty you will reduce participation in that activity. Common sense should tell you that without having to look at a study.
Basically I think you're looking at this issue in an ass-backwards fashion. You don't justify a regulation by first looking at how hard it is to meet. I mean, hell, why not require that anyone walking in public wear a baseball cap? It's pretty easy for anyone to get a baseball cap, right? What' the big deal?
Rather, you start by looking at whether there is a proven need for the regulation at all. Then, IF there's a need for some kind of regulation, you look at whether the regulation that's suggested to address it is reasonable relative to the scope of the problem, or whether, perhaps, the regulation might do more harm than good.
In the present case, there is next to no evidence that voter impersonation is a real problem in this country. It appears to be all but nonexistent. So the alleged harm that states are seeking to address -- elections that aren't fully representative -- seems to be made worse, rather than better, but imposing voter ID laws.
To the extent that there is any real voter fraud it appears to occur almost exclusively as a result of manipulation by poll workers -- rather than as a result of voter impersonation. So if voter fraud is REALLY the issue, why aren't Republicans proposing all kinds of regulations to prevent improper manipulation of votes by poll workers? It makes one wonder if their real interest isn't voter suppression rather than voter fraud.