Voter ID laws aren't about fraud. The amount of fraudulent voters required to sway an election would be a massive operation that could not be kept secret. But it's a distraction from the real issue: vote fraud by improperly denying people access to the ballot box.
Sure, you can get an ID cheap. Most of the time. But if all of your ID is lost (which can easily happen to the victim of a purse snatching) it's going to take time and money to fix the problem. And voter registrations are not supposed to be permitted to be challenged too close to the election. Not supposed to be doesn't mean it doesn't happen repeatedly, though. This scales much, much better than sending in fraudulent ballots. We find a handful of fraudulent ballots, often by Republicans trying to prove fraud is easy. 2016 and 2024 both had more people denied access by ID laws, challenges and the like than the margin of victory. And those missing votes would have skewed heavily Democrat.
Almost forgot: SAVE puts a very onerous paper trail on divorced women. They'll need copies of the paperwork changing back to their maiden name--something an awful lot of them don't have. I've already seen a variation on this with RealID. A mistake was made at my wife's naturalization, a hyphen crept into her name that didn't belong, went unnoticed for years. Even when it was discovered it was a so-what. Social security had an errant hyphen, everything else was as intended. No problem. Then RealID came along--and she had to do a legal name change in order to change her name to what her ID and passport said. Weeks and hundreds of dollars.
Denying legitimate voters is just as much fraud as permitting fraudulent ones. A system in which the the former happens at least 10,000x as often as the latter is not a good system.