Not really. How are you going to compute where somebody is on the poverty scale without an IRS? Somebody has to track if you have income and what it is. The IRS might be smaller, and only interested in the poor and near-poor, but would be that much more onerous because if it. You'll still have a lot of politics involved in setting the rules for meeting the poverty limit.
If the state of New Jersey were to write the rules, there would be location adjustment, and the poverty limit would be 80,000 in Hoboken, and 10,000 in Holmdel. Guess which party rules in each town. The national democrats would do the same thing, but would be more slick about it.
The only way to make this fair is to set the rate, and maybe exempt food & medicine. I really don't care if the rich get a cut on caviar to balance the general lower cost of milk. There's not enough caviar sold to be worry about.
Rebates are just another way for politicians to curry votes by robbing Peter to pay Paul. Let everybody pay, and then should you want to hand out government money, rather than calling it a 'rebate', call it charity, as that is what it is.
Income is still tracked and reported to the Social Security agency, and every purchases is tracked to make sure tax is paid. Keep all your receipts as they are proof that you paid your tax.