Voter fraud is close to non-existent. Even the most aggressive Republicans pushing this issue routinely concede this. This is not a matter of partisanship.Non-partisan researchers simply do not find any evidence of voter fraud.
In contrast, a variety of factors have cost Democrats whole elections. I suggest one review Greg Palast's great work on the 2006 election, the illegal disenfranchisement of felons in Florida that gave Bush the election in 2000, "challenges" and other illegal techniques used to win the election for Bush in 2004, and so forth. Voter fraud is not the problem: Government fraud is.
Restricting voting overwhelmingly harms the poor and the black and brown. No wonder it is being pushed by overwhelmingly white, rich people.