1. That each paper ballot was only counted once by the tabulating machine.
2. No extra ballots were returned with an id that was not generated.
3. Easily spot copied ballots.
You could probably audit more things. If for example the id corresponded to a county, and so on.
If the government mails me a ballot with ID #1234 on it at my home address, then they have a way of knowing that Ballot #1234 belongs to me in particular when they're tabulating the votes, which means they can find out exactly how I voted. Now we don't have a secret ballot anymore, and the secret ballot is a fundamental part of our democratic voting system; a secret ballot prevents the government from rewarding people or doling out punishment based on how they voted. It's a safeguard against authoritarianism.
(I think some US states put identifying info on the outer envelope or sleeve that the ballot is returned in, but there's a strict system to keep the envelope-opening step separate from the ballot-tabulation step, so people's votes cannot be personally linked to them as long as the system is followed. And these days there are usually cameras watching to make sure it is followed, and the footage is public.)
If you do get rid of the secret ballot then there's not much of a reason to hide the ballot ID via yellow dots. Just put "Ballot #1234" all over it and/or print a unique barcode. But regardless of whether the ballot ID is displayed or hidden, if you happen to get a dictatorial maniac into power (whatever you personally envision that person to look like) then you would be one step closer to letting that leader use personally-identifiable voting records to punish the people who voted the way he (probably a he) didn't like and/or give the people who voted the way he did like rewards or unfair advantages.
If you want to audit mailed out ballots, use two envelopes instead. The outer one will carry a unique id, the inner one will be completely anonymous and contain the actual ballot. All the auditing can be done on the outer, unopened envelopes. Then they are stripped off, all the inner envelopes are thrown on a heap and only then opened and counted.
Of course, even then, the paper ballots contain traces of the voter's DNA, so the truly paranoid will not be happy either.
> popularity contest driven by peer pressure
No, it's so people can't sell their votes, or be told by their parents/employer/local gangs that if they don't verify they voted correctly, they will be hurt. It's not cancel culture or popularity contests or whatever. Voting is definitely supposed to be a popularity contest based on peer pressure.
The completed ballot goes into an opaque sleeve devoid of identifying information, which then goes inside of an envelope. The envelope has an extra "flap" where you put your information and signature, and then it seals onto the envelope.
When processed, the flaps have perforations that can be physically separated from the rest of the envelope and validated and retained for audit purposes, and later on the collection of sealed envelopes can be opened and the ballots counted without having any attached personal information.
