For the majority of people out there, all their income is going to have digital records. A cash only store still deposits money in a bank, after all. For the people that don't... chances are their income without a digital footprint isn't being reported, and is small enough that no one is worried about that in the first place.
If the IRS is being told by a person's work how much they're paid, by their bank how much interest they got, by any Etsy-esque services how much they were paid... then the IRS has every bit of information it needs to get automatic withholding correct.
Right now withholding systems default to taking too much money out, because it's easier for the government to send you money than it is for them to request money from you. It also avoids the headache of most people being hit with surprise IRS bills. The IRS could keep that default, and then as the year goes on it could shift that withholding down until it's laser close. The negative there is that variability is bad for budgeting too, but with some work they could make it start close enough that it shouldn't be all that variable.