proponents of the banking bailout used this same rationale, that allowing big banks to fail would lead to economic collapse, but that was only the rationale, not the reason for that course of action. bernanke, paulson & geithner were instead worried about blowback to their careers and economic futures, because it would be their friends in high places taking the hit.
if some large banks had failed, most certainly other economic actors would have swooped in to pick up the pieces and resume business. these were lucrative, real assets after all. the danger was not in economic collapse, but in how long the rebound would take, and more pointedly, the effect on bernanke and friends' careers.
we retard progress and innovation if we don't hold institutions accountable and allow them to fail. bankruptcy is the mechanism we use to allow instutions (and people) to bounce back quickly from failure, so they can use their learnings to try another tactic.