Leaving the banks to go bankrupt would also be catastrophic for the economy as a whole, the banks know this. For the government to say "we'll let you go bankrupt" would be silly. Not to mention, the government will get its money back from that bailout, it's not like it's plunging money into a hole and its never going to see it again.
Separating the investment sector from personal banking however, would be a welcome regulation. It would allow us to let the bad investors to go bankrupt without it having an awful effect on the economy as a whole. To say that less regulation would stop them going bust doesn't make sense, all there needs to be is proper regulation that protects the economy, rather than bankers interests. Without this rule, there's no incentive for the banks not to make ridiculous bets. They know how powerful they are, anything else doesn't really make sense. As I said earlier, the question should be about the regulations themselves and one of the mistakes in the banking crisis was that the regulations weren't very good.