Eh lets not overstate it too much- this isn't the first time it has happened, paypal and a few other "internet banks" back in the early-mid 2000s was offering 5% interest rates when big banks weren't offering much. The big banks are as strong as ever.
Generally, you really shouldn't be keeping much in a bank anyway, invest most of your money, even if only in ultra safe bonds.
You can sell bounds, they can be fairly liquid, and the yields are higher, with a locked in rate for that time. Personally I am a bit concerned about the safety of keeping money at RH as well after their big F up last week.
The real point though was that IMHO aside from your emergency money, you should really have as little in cash as possible. My other callout was that high interest rates didn't appear to steal any significant business from big banks in the past.
Generally, you really shouldn't be keeping much in a bank anyway, invest most of your money, even if only in ultra safe bonds.