Isn't going to happen.
People vote their self interest,Younger people will prefer a flat sales tax since they don't have as much money to spend on "stuff", but older people will go with an income tax since they are no longer earning, or won't be much longer so they see it as putting the load on younger folks instead of themselves.
My earlier post was a trick comment, when the poor had to fend for themselves the poverty rate was the same as it is now, but the individuals in poverty changed at a much higher rate.
And until FDR and his socialist programs came along caring for the unfortunate was privatized, it was called Charity.
It is worth pointing out that after dumping tens of billions of tax dollars on the problem the percentage of people living in poverty has not changed more than a fraction of a percent.