....where, exactly, does that leave dems' argument that providing ID for voting purposes is a "hardship"?
I don't think that's the thrust of the Democratic (and "democratic") argument about voter ID. It's more about getting election results that are most indicative of the will of the people. When you set up hurdles to vote, you get fewer votes. The more inconvenient you make it, the fewer people vote. Requiring voter ID probably isn't inconvenient enough to result in a big drop in voting, but it does result in a drop. And, importantly, it results in a DISPROPORTIONATE drop in some kinds of voters.
For example, nearly all people in rural areas have drivers licenses, simply because it's needed to get around. So there's no added difficulty for them to show ID -- they've already got it on them. By comparison, lots more voting-aged people in urban areas don't have driver's licenses, since life in an urban area is less dependent on driving. And even if they have a driver's license, they're less likely to have it on them at the voting location , because they're less likely to have driven there than a rural person. So, you get a distorted election result: more votes from rural areas relative to urban areas.
That's just a single example. Younger people are also less likely to have driver's licenses than older people. Minorities are less likely to have driver's licenses than whites. Among older people, women are less likely to have driver's licenses than men. So, put these together and what do you get when you require people to show voter ID to vote: disproportionate voting power for rural residents, men, whites, and older people. Military personnel and veterans are also, of course, more likely to have photo ID than civilians (since they have to carry their military IDs with them to get access to various military or veteran benefits). Guess which party that benefits?
That is, of course, no accident. If young, urban, black female civilians were very likely to carry photo ID and old, rural, white male veterans were very unlikely to carry photo ID, Republicans would be against voter ID laws. It's just an attempt to skew results in their favor, just as, not all so long ago, poll taxes and poll tests were used to try to get election results that favored one demographic group over another.
Now, we could, of course, regard that skewing of our election results as a sad but necessary evil, if it were needed to combat rampant skewing of our results from widespread voter fraud. But, it turns out, voter fraud of that variety is exceedingly rare, to the point where there's never been any plausible case made that it has influenced any election results. Election fraud on that kind of piecemeal basis is just no way to steal an election. Elections are stolen by ballot-stuffers and others who find ways to over-count or under-count hundreds or thousands of votes at a time (like the Supreme Court in 2000), not by individual voters risking serious consequences for themselves in order to get a statistically meaningless advantage for their side in the election.
So, there's your choice. We can require voter ID in order to eliminate a phenomenon that skews results in a miniscule and meaningless way, or we can not require voter ID, and thus avoid a phenomenon that would skew results in a more significant way that could plausibly change election results. The choice, from a practical and moral perspective should be quite clear. Not requiring voter ID is the better choice, in terms of comparing legitimate votes deterred by ID vs. illegitimate votes accepted without ID. But the conservatives aren't analyzing it from a practical or moral "small d" democratic perspective. They're analyzing it in terms of expected partisan advantage, and there's no question that requiring voter ID is a partisan advantage for them.