This is not a criticism of Cruz' proposal, but IMO, retaining the home-mortgage interest deduction is a political calculation that will eventually return us to where we are. One deduction starts a cascade.
Further, I oppose charitable deductions simply because of the insane regulations we have crippling the economy at the behest of supposedly "charitable" foundations. Tax-exempt racketeering has become a monstrous industry feeding lawyers, greenies, and other bottom feeders. The scientific advocacy coming with it is ruining objective research. The day I see public prosecutors going after these wealthy leaches, I might change my mind. I know what this means to churches, but deducting contributions is asking others to foot the resulting increase in the tax burden.
Enough of all of it.
The charity solution is (if we must have an income tax) to have all entities pay taxes on their profits.
As it happens, churches and other charities don’t turn profits, so they don’t need to pay taxes.