The impact of tax credits, deductions, and progressive tax bracketing

I was interested to know if the government did not include ANY tax deductions or credits of any kind, and eliminated the progressive tax bracket, what the income tax percentage would need to be.  That is, every tax deduction, credit, and tax bracketing is in some way encouraging a certain societal “need”, or is flat out political pandering / cronyism.   How much does that shift the tax burden to those who do not claim those credits or deductions?
Examples of credits are the child tax credit and Earned Income Tax Credit.  Deductions include married filing jointly, home ownership deductions (mortgage, real estate), charity.  Tax bracketing is higher tax rates as income increases.  Essentially, if your tax return could be reduced to the “income” section on the first page of the Form 1040, then a percentage applied to calculate your income tax, what would that percentage need to be in order for the tax revenues to remain neutral?  That percentage then provides how much all of these credits and deductions are forcing those paying the 28%, 33% and 39.6% rates to pay extra to compensate for those credits and deductions.
 The closest I can find to a true flat tax is the Ben Carson flat tax.  He has a few deviations from a direct flat tax on the Form 1040 income section:
– $100 flat tax on everyone
– No tax otherwise up to 150% of poverty level.  He doesn’t specify if that poverty level on based on the individual poverty level ($12k) or graduated based on married ($16k per couple), or with kids (extra $4k per kid)
– No tax on cap gains or dividend income
– No tax on Social Security income.  Affects only upper income recipients currently.
– Adds employer provided health insurance costs to taxable income
Other than that, it is a basis for a true comparison if you were to eliminate all credits, deductions, and progressive tax bracketing.
Scroll down to Table 2, and it shows the shortfall in income tax revenues, both if the total wages were kept static, and for the Tax Foundation’s analysis of his plan and the resultant wage increases.
Here is the 2016 Federal Budget, with tax revenues at the bottom.
Carson does have an income tax revenue shortfall with a 14.9% flat tax.  But it is not by much.  If wages were kept equal (indexed for inflation), the flat tax percentage would need to be 18.5% to get the same tax revenue.  That is, income taxed at 28% is paying 9.5% extra (= 28 – 18.5), to compensate for all of the tax credits and deductions.  If the tax foundation’s analysis of the resultant wage increases are correct, the flat tax percentage would need to be 16.1%;  folding in increases to SS and Medicare payroll taxes, the flat tax would need to be 15%.  Note that this would support Carson’s claim that his tax plan is revenue neutral, but that claim is only true for income tax revenues.
On the corporate tax side, again there are a few deviations from a direct flat tax.  However, again there are corporate tax credits and deductions which he eliminates, so we can see how much these deductions and credits cost businesses who do not claim them.  If corporate income were kept equal (indexed for inflation), the flat tax percentage would need to be 27.6%.  The 27.6% is certainly far higher than Carson’s 14.9%, but much less than the current 39%.  Corporations who do not write off these credits and deductions are paying an extra 11% to compensate for those who do.  If the Tax Foundation’s dynamic analysis is correct, then the rate needs to be slightly higher, roughly 30%.
So that’s the story.  All of these tax credits, deductions and progressive brackets shift the tax burden to individuals and corporations who do not take them.  Whether their impact to “societal needs”, or political pandering / cronyism are worthy reasons, is left to the reader.