You still have to keep track of who has what account, changes of accounts, address, etc. You will still have a leviathan. Ever belong to a book club? (Do you thin the Federal Government is capable of operating at even that level of efficiency?) If not, it is going to be a mess, to put it mildly.
I repeat: the rebate mechanism is not a show-stopper. Far less complex than procedures already in place for other federal payments, as noted.