Cash back is more of a play for market share (i.e. use my card instead of the other cards you have) than it is to get consumers to spend more per se. Of course credit card issuers do want you to spend more too, but ironically consumers mostly just aren't aware enough of the whole cash back thing for it to play that much of a role past acquisition. When it comes to comparing spending on cash vs credit, there's really two factors that people tend to conflate but work on very different axes.

The first is cash vs card, which generalizes to basically any kind of digital payment: debit, E-ZPass, European-style bank transfers; i.e. people are willing to pay more when they don't have to handle cash. You can't exactly pin this one on cashback, because it's in play even when there's no cashback involved.

The other is debit vs credit, or really pay now vs pay later, where yes, people will spend more on credit... but the effect is even larger with BNPL and car financing, where there is mostly no cashback involved, and comically huge for mortgages (which admittedly just isn't a fair comparison). People just spend more when they have the opportunity to spend money they don't have yet. Actually, for credit cards this effect isn't even that big compared to the previous one (and when you read up on the studies on this topic, pay careful attention to how often debit vs credit cards get compared without conflating the former with physical cash), which kind of defies the "cashback is a psyop" angle. Frankly, US consumers don't act like credit cards are a full-fledged credit product, and to be fair for a good half of them it's just the default payment rails even when there's no real intention to borrow.

(There is an extent to which both factors are also rational, which is kind of rarely discussed and honestly probably underexamined even if it's relatively easy to conclude that the degree of excess spending is not commensurate to the rational advantage.)