It is hard to estimate the real ultimate effect of eliminating all the deductions, if only because of the sheer number of them.
As I noted earlier, the best estimates say that we could lower the "book" rate by quite a bit, simply because those deductions undermine the current stated rates of income tax on various levels of income.
If you have a rule, but allow almost everybody to be exempt from that rule, why bother with the fiction? I think it would be a uva lot more honest to just have a more firm rule with no exceptions.
The problem is that we pull the "lever" of the tax code to accomplish all manner of social engineering, from encouraging home ownership, to encouraging people to go to college.
It is an easy thing to do. We could just as easily provide direct payments that would be a bit more transparent, something I would be all for.