I agree with the overall premise.
But I had to wrestle with this more because I owned a point of sale company in 2010s...so, let's frame this to: if they are a vampire, how in the world are they still such a vampire 15 years later? As you put it more politely: what stops a big bank from doing whatever it is they do?
TL;Dr because they're middleman as in Switzerland, not middleman as in "pure dead weight"
No one has an incentive to cooperate with another big bank, and vice versa: they'd use rates competitively. Idk the proper game theory terminology for it anymore, but what comes to mind is "unstable equilibrium"
In this structure, all the incentives are aligned. Banks neatly separate out deposit customers from customers receiving credit, so you don't get pissed off at them if you get behind. The middleman wants to charge as much as possible, below the price where the bank is happy to take on reputation risk.
I also cannot 100% confirm this, but I think the case you're presenting is too simplistic. Ex. doesn't ring true to me there's no credit extended. Maybe they securitize it, but ex. AmEx is the one giving me up to $CREDIT_LINE to spend, unless, I've been missing it all along and the credit cards are opaquely funded by other institutions. (Wouldn't surprise me, older I get, the more I see things I've managed to miss for 36+ years)