A worse version of this that I've read a few times is banks suddenly "security" flagging your accounts and disabling everything for sometimes up to weeks at a time while they "investigate."
I've tried to protect myself from a single banking point of failure with this setup:
- Paycheck into local Credit Union Checking
- Partial automatic transfer from Credit Union Checking into online Bank Checking
- All bills are paid from the Credit Union except Credit Cards, which are paid out of online bank
Ultimately if either the Credit Union or online Bank has problems, I just use the other one. I'd then move my next months Paycheck if it was the local Credit Union that was problematic. This setup is actually simpler than I am making it sound, two checking accounts and a single automatic transfer (then splitting your bills appropriate).
Nobody should have to do this to have a good banking experience, but prudence never hurt.