The suggestion here is to not change the complexity of the taxes themselves¹. The suggestion here is to change the complexity of filing those taxes. You can keep all the same credits & deductions that exist today, but still move to a system where the IRS says "here's what we know about your tax situation, are there any adjustments to be made?". For a large majority of people, that latter half is pretty small.

But that's a simpler procedure than forcing them to compute most of what the IRS knows from scratch.

¹But if you want to, that's fine too, it's just not what this thread is about.