At least here in the US, even children have tax IDs. I don't think it would vanish completely, but it makes it a much smaller issue when all you have look for double-submitted tax IDs instead of running heuristics.
I think the unique ID system should be fixed (without damaging privacy); we have the technology to fix IDs to identify people and let them ID themselves or do KYC without the current fraude prone and error prone setup. I understand this is a big undertaking, at the start, but in the end, it will be easier for most people, harder or impossible for fraudsters and easier for the government. Indeed having a unique UUID assigned at birth or when moving into the country is a first step and trivial to check for even if it is, in essence, anonymous.
Systems similar to this exist. They’re not (all?) anonymous, however.
Every Swedish citizen and resident has a unique and dedicated number (date of birth followed by four digits), and you can use it in tandem with for example BankID (https://en.wikipedia.org/wiki/BankID) to authenticate yourself almost everywhere.
It would be extraordinarily hard to make up UBI claims for non-existing family members and receive payouts in Sweden. You would first have to convince the tax agency to register the fake person in order to get a new personal number, either as a newborn or immigrant, which either way is obviously subject to controls. You’d then have to keep this up through various mandatory interactions with government agencies without getting found out. It would probably be much more effort (not to mention stress) than just working for the same money.
How would you manage to register 5 fake family members with the government? Governments already track its citizens in basically every country, it is really hard to trick them into thinking more people than that exists.
"Social Security records show that 6.5 million people in the US have reached the ripe old age of 112. In reality, only few could possibly be alive. As of last fall, there were only 42 people known to be that old in the entire world."
It's not just dead people.
"One Social Security number was used 613 times. An additional 194 numbers were used at least 50 times each."
Its more like not registering the departures of family members from this mortal coil, and is a persistent (if relatively small scale) problem with Social Security payments in the States.
Which, one again, circles to the point that the money, time, and effort spent on fighting such low level individual fraud typically vastly out-spends the actual fraud they're trying to combat.