Edit: maybe I wasn't clear and should have said "between" banks. Synchrony bank will give you 4% in a _savings_ account (https://www.synchronybank.com/banking/high-yield-savings/?UI...) while my local credit union and many big banks (ex: bank of America are at 0.01%) are still effectively 0%
In the past (<2008), cash accounts (savings/cds/etc) I remember there being a %1 or so between banks, but these days its huge.
That's really the big reason why savings rates vary so much between banks, if you have a bunch of consumer credit lines then high savings rates make sense, if you have a bunch of lower fixed-rate collateralized loans then you can't get away with lowering your spread so much.
There's other epicycles to this too. For example, a bank can just "buy" deposits through a correspondent bank (a bank-for-banks). So the direct connection between your kind of borrowing and kind of lending, particularly when its consumer / credit card stuff, can be tenuous. In SVB's case, though, all of the stuff happened in a tight echo chamber ecosystem -- SVB got deposits from tech cos, who got money from VCs, who were working off of capital call LOCs from SVB. So your observation is germane.