The way I see it, the bigger problem is that big banks are immune to the free market, as they will just get bailed out by central banks any time they fail. It is a feature, and not in any "banks are inherently terrible" way. It's a feature in the sense that banks will gradually become more stable and niche, working only with the things they ought to and reasonably can, instead of flying by the seat of their pants and waiting for the Fed and FDIC to save them.
TLDR, not an inherent bank issue but a moral hazard in our modern system issue.