Only the consumer needs to do so in this case, not the government, and if you don't keep track of your own purchases, no problem, you just don't get the rebate.
Tracking purchases requires time and skill, both of which are often lacking in the poorest. Rich would hire a person to do it. (and also to game the system)
Not really, no. Or rather, the ability to do that is not so much tied to wealth as education and upbringing: you have to be functionally literate and numerate in order to do that, and many of the people who would need the most support aren't.
Many more have the basic numeracy but lack the background to plan finances at all. The UK government recently changed the way they pay rent for people with housing benefit. Instead of direct to the landlord they pay a lump each month, while rent is typically due weekly. Many have fallen into arrears as a result: they didn't want to be given the money, and they don't know how to deal with having a balance in their account that they must budget.
Perhaps you might consider someone unable to cope with that change unworthy of support, but when there's a whole class of affected people I don't think it's helpful to write them off as a group, rather than trying to understand the reason why they find it hard and trying to set up the system to mitigate those difficulties -- just like if your users fail to understand a feature in your project, you'd be wise to redesign it to be usable. Only with somewhat higher stakes.
