Capitalism depends on competition.
Competition depends on the risk of failure. A business "too big to fail", by definition, is immune from the risk of failure and so is immune from competition. Therefore, a business "too big to fail" is not a capitalist business.
Institutions too big to fail, like governments, are held accountable by the governed through elected representatives.
Any business "too big to fail" is beyond the market's influence. Owner self-interest reigns unchecked. Public regulation is then required in its place in order to mitigate the natural drive to predation of competitors and exploitation of customers.
Without significant competition or government control, a company that is "too big to fail" cannot help but economically prey upon the all in its single-minded pursuit of profits.