If you listen carefully to the "ballot access" side of this argument (actually informed people and politicians, not random on the internet), you will see they don't ever say it does not happen.

What they say is that it does not happen enough to plausibly come close to affecting the outcome. And this is widely supported, including by right-wing organizations (as a sibling comment observes).

As with most issues, there is a trade-off here. As you tighten controls to prevent improper voting, you prevent some people from realistically being able to vote (it's just too hard, time consuming or expensive for them to meet the documentation requirements), and discourage others. This is particularly bad for the 1-2 elections after the rule change, which most people won't know about until they show up to vote. IMO, this is really the point of the changes.

And you have to weigh that negative against the supposed benefit. But that benefit is really hard to find. It's very clear that intentional voter fraud (fraud in registration, or in-person impersonation) is extremely rare, and does not come anywhere close to affecting outcomes. It's already a crime, and we seem to be pretty good at catching it.

The other argument for a benefit is that it improves voter confidence in elections. I reject this, since the only reason the public at large has any real concerns is because of intentional misinformation by the right. You can't lie to people to convince them there is a problem, and then use that to justify your heavy handed solution.