The federal insurance program made it so people could trust in banking again.
Now I do think that the policy has gone too far. Bank investments should receive any bailout, those are part and parcel of the normal functioning market.
The real laws should have been 'banks shall not loan out money from a depositor's account' and the problem would have been resolved. Investors could have loaned out money. Insurance could have protected against bank robberies, similar to how any kind of insurance works against theft today.
In this situation though, when there is a threat to society as a whole either military or natural, there’s a legitimate role for society to pull together and coordinate our actions. That’s what government is for. All societies can benefit from consensus and leadership, especially in situations like this.
If their business model really fails, then fine, that’s because there’s enough value in alternative providers that these ones are no longer needed. However in temporary crises it’s possible that the process of dissolving businesses can leave a gap in the provision of valuable or even vital services that the market cannot fill fast enough. Markets are incredibly powerful, but they aren’t omniscient or omnipotent.
This is why although I’m a believing capitalist, I think there is a role for regulation and even bailouts in extraordinary circumstances. I’ll even extend that to individuals, a crisis can hit any of us just as it can hit a business. I don’t see that necessarily as socialism, just good management when done judiciously and proportionately. Ultimately it’s about fairness and good outcomes. I’ve no time for ideologies.
And, in this fun world, you might find a terribly over-leveraged business where no one ever tried to act fraudulently but some vulture capitalist consultant helped "ensure access to liquid assets" and is now in Kiribati watching the world burn.
In practice, I think we will see companies being sold off the friends of the sitting president, and powerful senators.
Today, at least they must at least pretend to be equal in their bailouts, which gives non affiliated companies a chance to receive money.