I thought the flat tax system was a percentage of income, just the same for everyone and that means the rich would pay more than the poor. I suppose if you could sequester the government budgets into programs that benefitted everyone equally and tax everyone equally, it would be nice but I’m not sure it could be done with any degree of logic or fairness and practically, I doubt any government would assent to being hamstrung by such sequestration. (Just to give an example: do the poor or the rich benefit more from urban renewal? You can argue that both groups benefit and then start quibbling about how much. It would be an endless and rancorous debate and there are thousands of such programs which arguably benefit both poor and rich.)
Give a man a fish, he'll eat for a day. Force everyone in the village to give him a fish, he'll vote for you in the next election.