Ordinary deposits with banks should be protected by the government because the general public cannot evaluate the risk of a bank collapsing. There's probably a case for some protection for companies that hold accounts -- although companies should really be aware that by depositing money in a bank, they become lenders to the bank, and they should have the skills to mitigate that risk. Perhaps smaller companies, and accounts specifically holding payroll, should receive greater deposit protection.
Which seems to translate, at least in my mind, to 'banks should be too big to fail, but only in the ways I like'.
It's not clear, under your scheme, how we would draw the line between companies that "should be aware" of the risks and how they would mitigate them? Do we have to have insurance policies against our bank deposits? But who pays for that?
Maybe I'm not reading with enough goodwill here though. Perhaps by "the government should protect" you mean to say something like 'there should be laws / regulations making it so that banks shonky investment dealings can't affect depositors accounts, at least for some class(es) of depositors' - in which case I agree.
I didn't say any of that. Banks should never be too big to fail. The only question is which of the bank's account holders should the government preferentially bail out by printing money equivalent to the holders' deposits.
Regardless of the actual dollar amounts changed hands, what the US Federal government demonstrated was that risky - even illegal - behavior will be covered and some losses will be covered. It means that next time (and there will be one), we should assume the risks and losses will be even bigger.
But more seriously, why did the resolution have to be a bailout. Could someone with the authority, and here I mean The Government, because they've got the guns, just tell the banks to rollback the wonky transactions?