The problem is there's an assumption that the government data is right, and disproving their data as a taxpayer would be tough. (Fighting city hall is tough)
In the current voluntary compliance regime, a very small number of returns receive audit treatment of any kind.
A few years back I miscalculated my self-employment tax. Didn't get audited, just got a letter saying "You miscalculated and overpaid", followed by a check for the $100 or so.
The government can disagree with your return based on their data without auditing. A couple of years ago, the government told me they thought I'd under-reported my taxable income from a couple of years earlier (I had, because a place I'd worked had failed to give me a 1099). I wasn't required to undergo an audit; they just said they thought I owed this much money and I should either pay it or explain why I didn't actually owe it.
well the UK system seems to work well I got one rather complex tax situation sorted out with a single phone call.
Previous employer went bust the hard way so I had a couple of tax years where my income was up and down - I rang up got though quickly the operator on the other said ok yes your owed xxxx we can change your taxcode for most of it and for this tax year you will get a refund after the tax year end.
I was expecting to have to take lots of calls and take several months to sort out.
The more information you have the better. You could still dispute the numbers the IRS. I fail to see any downside in such a system (other than for TurboTax and CPAs)
Even a 1% error affects over 3M people.