Chase doesn't allow storing cash in them (other than collectible items) and I know that others banks don't allow either (most likely to limit their liability).

I lived through Washington Mutual going through FDIC receivership back in 2008 (I was their employee, shareholder and account holder at that time) and their stock price dropped to almost zero when the news broke about that. I'm curious why this is not the case here.

No, not a safety box. A bank. Like the other ones but without them playing bets with your money. That's literally it.