Voter fraud on the counting side can be countered by recounts, which would likely occur in this day and age in a close election.
However, if operatives discovered they needed votes in a very close race, they could send people around to various polling places and have them claim to be people who hadn't shown up yet. If this were done near the end of the day, it could be effective.
I'm saying that there's no point to leave this possibility open because a very small percentage of the electorate doesn't feel like getting ID.
I would even be fine with waiving ID processing fees for low-income people and making it easier for them to get ID. But allowing non-ID voting is a terrible idea, and contradicts our otherwise ID-dependent society.