If you really want to cap income tax, why not make it simple and have a flat tax?
The progressive tax scheme is just a shell game. Heck even your plan, assuming 100k of income, filing jointly, with two kids, is about the same as it is now (actually I think your way is a touch higher).
If we have to have an income tax, it needs to be flat and needs to apply to all income (make one dollar pay 10%, make a million pay 10%)
The last, and in my mind the most important part, is to remove withholding. Americans are numb to taxes and since it is taken from the check before they see it, it does not burden them. Burden the American tax payer with tax collectors at their door, and I think you will be surprised how many Americans start caring about where their hard earned dollars are going.
“why not make it simple and have a flat tax?”
Our country has traveled too far down Communist Manifesto Way for absolute flat rate taxation.
Lower income people often pay large percentages of their income in sin taxation.
Bear in mind, the refundable tax credit schemes are the worst feature of our system.
Government would never allow withildings to be discontinued because it is too convenient of a method.