Capital One, Discover, Ally, etc. were offering 4.35% at the peak. Not quite as good, but very decent for a savings account.
I don't know where you would draw the line under "major", though. But everyone knows BoA, WF, and Chase are trash when it comes to savings rates. They don't do it.
In Europe, HSBC (which is comparable in size to Chase and BoA) has reliably high saving accounts rates. HSBC UK was offering 5% until recently, I believe.
[1] https://www.fidelity.com/spend-save/fidelity-cash-management...
[1]: https://www.usbank.com/bank-accounts/savings-accounts/elite-...
These banks are up front about not competing on rates.
They promote their savings accounts with opening bonuses, offer bonus rates for high net worth account holders (up to 0.04% instead of 0.01!!) etc.
Transparency would be not calling these terrible offers "savings" accounts (or sometimes even "high-yield savings accounts!") in the first place.