Synchrony offers such high yields on savings because their big product is consumer credit cards, and even at 4% APY on savings accounts the spread to a 25% APR credit product, even factoring in risk, makes it extremely profitable to do so.

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.

It's not nearly that simple, though. You are ignoring capital requirements. For things like Treasuries, you don't need any capital % against it. ($100 in deposit -> $100 in Treasuries, if you borrow at 1 and lend at 4 you made a 3% spread on $100). But for risky things that might yield much more, you might need to reserve far more, meaning you need to fund part of it with equity. ($100 in deposit but with a 50% capital requirement means you can -> buy $100 of high-yield stuff, but you need to use $50 of your equity to do so)

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.

Yeah, I oversimplified it to a large degree because getting to deep into the nightmare that lies beneath the banking system can make ones head explode. It's accurate enough for a layperson, if nothing else.

Not exactly. The banks do not want less deposits (ask SVB how bad that can be!) but they try to get away with paying as little as possible and keep the spread. (You wouldn't say that the main objective of companies when they raise prices is to have less customers, would you?)

If they wanted more deposits, why would they pay as little as possible to 'keep the spread'? No bank is anywhere near monopoly; there are tons more deposits to get (if you want them, and can make money safely on a spread).

For the same reason that many businesses do not want "more customers" above anything else - to the point of selling at cost or at a loss - and if they increase prices is not necessarily because they want "less customers".

Some banks actually do want less deposits. They do things like increasing fees to chase them away. But it takes some real discipline and investor management to pull it off.