While that's hard to predict with absolute certainty, an economic collapse in which many banks fail, as in the Great Depression doesn't seem to be anywhere on the horizon right now. If anything, the economy is super heated right now, which is why the Federal Reserve is trying to cool things down. Most people don't realize it but bank failures are not that uncommon. However, in the past the federal and state regulators usually resolved troubled banks quietly, usually having another, stronger bank take over the failed institution. So most of these bank problems don't make much news. And the failure of a bank every so often isn't going to cause economic collapse. The problem in the 1930s was there was no deposit insurance, no consistent regulation of banks, and no plans in place to deal with bank collapses so the savings of the average person could, and did, get wiped out in the infamous runs on the banks. We see a scene of that in the classic holiday movie "It's a Wonderful Life" starring Jimmy Stewart, one of the finest actors Hollywood has ever seen, IMO. Since the creation of the FDIC, so far no person has ever lost any money in a bank failure.
But economic collapses can sometimes occur very suddenly with little warning. So for persons who have more than $250,000 that they want to stuff into a bank account (which is not a great way to invest, btw) it makes sense to split that among different banks to get all your accounts insured.