This is a complete misunderstanding of the problem.
I invite you to read Taleb (I'm not trying to sound like a fanboy; but his ideas are literally the utterly common-sense conclusions you'll reach if you study complexity science as applied to the financial system; i.e. they are objectively and necessarily true).
I'll try to present a very simplified but rigorous case:
1. There's commercial banks (that take consumer/corporate deposit & give out loans), and investment banks that arbitrage the markets. If you allow banks to fulfill both commercial and investment roles, consumer deposits are at risk from bad investment decisions. Note that Glass–Steagall is still repealed, and banks are still allowed today to put your money at risk.
2. Many investment banks used mathematically-flawed risk models, that underestimate fat-tail risk, and therefore lead to inevitable collapse. Read Jim Rickards's testimony to the House of Representatives on this; he was LTCM's general counsel, and LTCM (a who's who of finance PhD's and Nobel Prize winners) blew up due to overconfidence in these flawed models (https://moam.info/house-testimony-rickards-committee-on-scie...).
3. The problem here is systemic risk: banks only get rescued because they're systemically important. "Systemic-ness" is mainly a function of interconnectedness of markets, i.e. systemic banks cannot fail without destroying the markets and economies. Hence banks have an incentive to become systemically important, so they'll get bailed out if they make mistakes. Risk of catastrophic system failure is incentivized.
4. Small banks failing is normal. FDIC insures deposits to a certain amount; no Average Joe gets wiped out, bank investors do. The key point (covered in Taleb's Antifragile book) is that individual survival (agent) and ecosystem survival (system) are often at odds. Animal evolution requires death, since that's the filtering process; if everyone survived, no natural selection occurs, no evolution, and pathological mutations would eventually accumulate and wipe the species out. A healthy banking industry is one in which banks fail regularly, without impacting consumers (thanks to FDIC), and where bankers who worked at those banks get wiped out financially too, and don't just walk away with bonuses. Then, they'd have an incentives to stop using known-defective quant risk models. Contrary to popular opinion skin in the game isn't about incentives but about filtering (if you fail at the game, you personally suffer the consequences and cannot continue playing).
Many problems in the world stem from misunderstandings of either complex systems theory (an actual scientific discipline that should be taught in high school), math (mostly dimensionality and fat-tailedness) and probability theory. Without a basic understanding of these, people simply don't have the tools to understand or discuss much of the modern world.
The consequences can be seen in systemic financial failures; in ineffective pandemic responses; and in much of social science. See for example:
https://arxiv.org/pdf/2007.16096.pdf
https://arxiv.org/pdf/1505.04722.pdf