Because doing public works doesn't help get the person to be self-supporting in the long run. Right now, you're required to spend your time applying for jobs, getting training, etc to collect unemployment. And regardless, you will be kicked off after a period of time. You can't buy beer or cigarettes with food stamps. But in terms of "properly", I was meaning using it as a temporary form of support while looking for a job.
If the income tax was the only tax in the country, you would be correct. unfortunately, there are many other taxes and all of them affect the poor and middle classes more than they do the wealthy, which is the entire reason that the income tax was made to be progressive in the first place.
The only place you are right is when talking about the uber-wealthy, whose income is derived from investments. They would end up paying more because of the Bush tax cuts, which reduced capital gains and carried interest tax rates to 15%. For the wealthy who earn their money, tax rates would go down (if you brought the tax rate down 15% in your example or 10% in JD's example) while the middle class, whose tax rates are already around or below 25%, would see their taxes go up if things like the mortgage interest deduction is eliminated. The income tax is progressive because all other taxes are regressive. Talking about a flat tax without considering the regressive taxes is a non-starter.
