Despite many instances of electoral fraud internationally, in the U.S. a major study by the Justice Department between 2002 and 2007 showed of the 300 million votes cast in that period, federal prosecutors convicted only 86 people for voter fraud – and of those few cases, most involved persons who were simply unaware of their ineligibility.
I would draw attention to the fact that this study was conducted by the Bush administrations Justice Dept.!
Electoral fraud - Wikipedia, the free encyclopedia
Killing one person is murder, killing 100,000 is foreign policy
And the bolded part just isn't true. The people who are registered and do not have the acceptable forms of ID obviously DO NOT NEED the required forms of photo ID except to vote. If they had to have the required ID, they'd have it. The rules require 600,000 properly registered Texans to spend money on an ID they do not otherwise need. Hence, the "poll tax" nature of the law.
And 2) no one disputes that these roughly 600,000 people in Texas get by just fine without the types of Photo ID required in Texas to vote. So your question is interesting from a sociological standpoint, but irrelevant to the discussion of photo ID for voting purposes.
And the thing is, if you were going to vote as someone else, why show up at the polls and risk showing your face? Request an absentee ballot instead and you need no ID, and don't risk someone who knows Jane Doe is at the desk when you sign in as Jane Doe. Of course ALL the evidence indicates that in fact those engaging in "voter" fraud do it through absentee ballots, naturally. It's less risky, by far. And Texas and most other republican states passing strict photo ID laws did NOTHING to tighten up the rules for absentee voting.