I'd expect if we moved towards a direct-bill model, tax policy would begin to optimize for "causes least frustration for the 200 million common-case taxpayers who do the direct billing."

We'd probably see more monkeying around with the standard deduction. I know for me, and presumably a lot of people (especially those without major mortgage interest), the current standard deduction exceeds the benefits to be had by itemization-- and claiming the trivialities like charitable donations or medical expenses.