Since you opened the door...A flat tax would not mean the elimination of any revenue department. However, a leaner and more efficient IRS would be the way to go.
The problem with that idea is that money invested into the IRS returns tax revenue at a rate of about 6 to 1. So if you invest a dollar in the IRS, they collect 6 more. Cutting the IRS wouldn't result in overall savings. It would result in a net loss.
What cutting the IRS does is make it easier for people to cheat on their taxes. Which I suspect is the point.
BTW, the IRS does not check to make sure one pay the correct amount. In fact over 90% of returns are not audited.
With no IRS as Ted Cruz proposes, you wouldn't get even that 10% of audits. There would be no enforcement. Like speeding laws with no highway patrol. There's no one to issue tickets. Even if only 1 in 10 returns are checked, that's still an enormous deterrent to tax cheating. As the likelihood of being caught would be 1 in 10....each year. And if they catch you, they'll likely go back half a decade and look at past returns.
Be eliminating the IRS completely, you make it vastly easier. Which again, is the point. Its no coincidence that Hedgefund managers are bankrolling Cruz's superPACs. They want to eliminate as much enforcement of tax laws as possible.
The IRS has morphed into a gigantic bureaucracy. And now, as we have seen, a took for this POTUS to use as a weapon against those who defy him.
Save for two problems: the IRS returns more money than is spent in on it by a factor of 6 to 1. And the POTUS using it as a weapon against those that defy him is an imaginary narrative. Take the whole 'IRS scandal'. There's no evidence of POTUS involvement. No evidence of any political motivation.
Oh, there are the accusations. But the evidence to back them never materialized. Yet instead of abandoning the accusations when the evidence didn't back them, the accusations are merely repeated without evidence.
That's not a rational basis for defunding the IRS.
The various depts of federal government exist to serve the people. The IRS serves itself and its master. The time for a rewrite of the US Tax Code has arrived.
We're not doing a flat tax for all the reasons you avoided. That it shifts the burden of taxation from the wealthy to the middle class and eliminates most of the middle classes largest exemptions.
Its where the 'flat tax' narrative always breaks. And will continue to break. Which is why it won't happen.