Invert your thesis, from “the rich are so rich because they spend less money” to “the poor are so poor because they spend more money”, and it becomes much more defensible. Boots theory captures the “being poor is expensive” element that’s true in Ankh-Morkpork and also true on Earth—look at the markups on any household item when it’s sold individually rather than in bulk, and then consider what happens to people who don’t have what it takes to plan ahead and make bulk purchases.
If we’re being particularly literal about things, Ankh-Morpork canonically lacked fiat currency until the events of Making Money, so we might want to consider the other ways in which their economics functions differently from our own. They also have magic, and the deities who implement their laws of nature sometimes pop round for a cup of tea. So I wouldn’t rule out that Vimes’s use of boots theory as a full explanation for economics could be less descriptive than prescriptive—he lives in a world where enough people believing anything hard enough makes it real.
Where is it cheaper per item to buy the same food or household good singly rather than in bulk?
Where can you get a single roll of the same toilet paper for less per roll than getting it in a bigger pack? Ok, now what if you need TP and the cash at your disposal at that moment is less than the cost of the bulk pack but more than the cost of the single roll?
When is it cheaper (time + money) to cook one meal at a time versus meal prep for the whole week? OK, now what if you can’t afford the whole week’s worth of food at once?
We might be talking about poverty at different orders of magnitude, and you might be writing off a lot of failures to purchase efficiently as “skill issue”… but being poor in skills and the capacity to hone them is, itself, a form of poverty.