The main point is that when its know that government will offer a bailout to banks, it generates moral hazard. Banks do not face the full consequences of profligate lending and therefore, engage in speculative mania.
Furthermore, bankruptcies have the salutary effect of transferring resources from failed entrepreneurs to successful entrepreneurs. Bailouts are counterproductive to the restoration of efficient resource use. They subsidize inefficient entrepreneurs.
Bank financing makes up less than 1/4 of all capital funding in the world economy. Even a collapse of banking would hardly dry up all capital funding.