The problem was SVB was a "specialized regional institution." The Washington Post points out depositors would've been fine in a normal bank (citing a Washington financing consultant):
"Where SVB relied upon tech-focused venture capitalists for much of their funding, larger banks have millions of depositors, access to wholesale funding markets and interbank channels... Regulations that were tightened in the wake of the 2008 financial crisis also have left the banks better armored against potential dangers. The Dodd-Frank Act required banks to hold more capital in reserve, as a buffer against unanticipated losses. At the end of September, JPMorgan Chase reported holding $236 billion in Tier 1 capital reserves."
I'd also like to second the commenter above who said SVB may be bought by tomorrow -- with all its deposits being honored, and no one losing anything.
In fact when I first read this thread's headline, I thought you were asking the "prisoner's dilemma" question. Because if all of the depositors had left their money in SVB, the run wouldn't have happened. SVB actually had lined up stop-gap funding, Reuters reported. But then "Some SVB clients pulled their money from the bank on the advice of venture capital firms such as Peter Thiel's Future Fund... This spooked investors such as General Atlantic that SVB had lined up for the stock sale, and the capital raising effort collapsed late on Thursday."
https://www.reuters.com/business/finance/what-caused-silicon...