Bank failures were incredibly common in 19th and early 20th century America. Today they are next to non existent.
Again, take a step back from the ideology and look at the evidence. The count of bank failures before 1930s era regulations vs post speaks to the effectiveness of government intervention.
That's a bit of a circular argument, since there are radically fewer banks now than there were in the past. Just in the last 20 years the number of banks in the US was cut down in half; and back in the 1930s, there were almost four times as many banks as we have now. Fewer banks mean fewer bank failures.
A fairer comparison perhaps would be to see how many dollars of deposits (in some adjusted manner, like per capita, percentage of GDP, or percentage of circulating money) were imperiled as a result of bank failures back then versus now? A hundred banks failing in the 19th century each serving a few thousand customers each would be a much smaller impact than, for example, the hypothetical failure of Bank of America.
Bank failure is a different problem than bank consolidation, of course it would happen less when you don't allow small banks to exist and just give money to the ones that do so that they don't fail, making them richer and protecting them from their mistakes
Banking is already one of the most regulated industries, regulation takes out smaller companies and leaves out only the ones that are big enough.
It seems to me way more dubious to claim that more regulations would solve this problem in an already incredibly regulated industry