Yglesias points out that tax deductions have widespread popularity (not just favored by a narrow interest group) and would probably get replaced by an actual government expenditure if they were cut out:
The main point I would make ...is ...how hard tax reform is. This is often portrayed in DC as if it's primarily a political difficulty, like the problem is simply that politicians lack the gumption to take on the interests behind these tax breaks. But part of what we see here is that many of these really high-value tax breaks are integral elements of American social policy. Take the charitable deduction, for example. All governments in the developed world do a lot to subsidize things like universities and museums and other cultural institutions. In the United States, the availability of a tax deduction for charitable contributions is one of the main ways we do this. Rescinding the deduction and replacing it with more direct subsidy along European lines is a proposal that might make some sense (although I don't think I would favor it) but simply eliminating it in order to finance a tax cut would be an epochal change in education and cultural policy and not just a tax shift.
An even stronger version of this occurs with the health care tax deduction. Subsidizing employer-provided health insurance and then regulating it is not, in my view, a very smart way of providing health care insurance to people. But it is the way we've chosen to do it for the non-elderly non-poor population. To replace this way with some other way would be a great idea, to just eliminate it and replace it with nothing would be a disaster. The EITC and the Child Tax Credit are two of the main instruments of income redistribution in the United States. There's a case to be made for scrapping all of this stuff, but with the exception of the deduction for state and local income taxes I don't think you could do any of it without creating some kind of new replacement non-tax policy.