That's semantics. If you call it a prebate, would it mean any thing different ?
Checks would get issued to every household each month. The timing of when you purchase your necessities (before or after you get the check ?) is nobodys concern but your own.
Each household would register once, and again as circumstances change. New children, older kids move out, change of address, etc.
And those who want to drop off the screen completely wouldn't register in the first place.
The reason to avoid exemptions is it will short-circuit politicians and special interests from playing with the code to their advantage. An example : for many years in Texas kiln-fired portland cement was tax-exempt. Milk and bread are taxed but not "kiln-fired portland cement".
This is not something that should be repeated on the national scale.
We need to make it lean, and that is why I am in favor of a flat 10% tax instead, simple arithmatic to check returns, simple arithmatic to teach people what they owe and pay.
Graduated taxes are wrong in any sense.