Something I did not realize until recently, which I think is very important here, is that the FDIC is not funded by taxpayers. It is funded by fees levied against the banks themselves.
https://en.wikipedia.org/wiki/Federal_Deposit_Insurance_Corp...
I'm sure that's not passed onto the customers at all.
Its the same failure mode regardless if played via everyone paying taxes or everyone paying FDIC, privatize the gains and socialize the losses until collapse.
But if everyone is paying FDIC via fees levied against private banks, then the POTUS and Yellen and everyone else can release a statement saying "no taxpayer funds will be used to bail out SVB". That way everyone can breathe an ironic sigh of relief: "Oh good, I was worried I was going to have to foot the tax bill for that. It's bad enough I have to pay all these greedy capitalists at my local bank a new fee every other week, at least the government is looking out for the little guy!"