> their pet things that are obviously worth complicating the tax code to do
I agree that this is at the root of the problem but I think that can be addressed by making it easier to file taxes or by reducing the complexity of the tax code. The child tax credit is a relatively common type of benefit across rich countries. The tax code could be simplified by administering this benefit via direct cash transfers through a different government agency. I think from this perspective, the IRS is _extremely_ efficient at benefit administration.
My personal opinion is that the tax code is not always a bad way to administer benefits but the paperwork burden is the problem and the experience of filing taxes needs to be made easier.