What you’re thinking of is FDIC which is completely the opposite of a bailout for the bank. It’s a bailout for depositors (a huge portion of which were normal people). Arguments for the FDIC protecting people from keeping money in bad banks is a different argument, but it most certainly isn’t a bailout.

If you think going bankrupt and the FDIC seizing your company and wiping out shareholders is a bailout, you don’t know what a bailout is at all. That’s standard bankruptcy with an extra heavy boot on the throat from the government because they are ruthless about maintaining consumer confidence in the banking system.