If a close match were demanded, people would complain of disenfranchisement. People don't sign the exact same way every time.
Realistically, the workers are tired and they don't care. If they do reject anybody, it's probably because the vote comes from an area that tends to vote in the undesired way. In other words, this human element is a problem. It would be especially easy to bias the election by rejecting based on name.
An imperfect signature of the desired ethnicity (more likely to be a "correct" vote) gets a pass. An imperfect signature of the undesired ethnicity is a fail. That's all it takes to quietly flip an election, with no evidence trail at all.
For vote-by-mail though, how could anybody go to jail? The ballot shows up. It is accepted or rejected. If rejected, then what? Are we going to pick fingerprint DNA out of the paper fibers for this? There is no reasonable way to ever determine who attempted to cast the vote.
It'll be fraud, but never part of the official statistics. It can't be proven without using the level of resources normally reserved for famous murder cases.
There just isn't a deterrent. Severe punishment means nothing if the criminal thinks he has no chance of being caught. The fraud can be done in bulk, and it is, via ballot harvesting.
Also, what about the corrupt verifiers? Being prone to rejecting some names more than others can change an election, and there would be no way to prove it. If the signature verifier has a preference between Cohen and Abdul, or between Garcia and Washington, what can anybody do?
With the mail-in voting, the person isn't present. You can't possibly find the person. No matter how obvious the fraud, there is nothing to be done about it. The person is certain to avoid arrest. No charges will ever be filed, and some people will then conclude that fraud doesn't happen.
In the one case, the criminal faces a small risk that is easy to dismiss. In the other case, there is no risk at all.