It sounds like you're talking about eliminating things like the FDIC, which is crazy. People (and banks) suffered tremendously before bank regulation evened out the business cycle. Then they decided to ease things up and let banks play around with depositors' funds, and within a decade we had the financial crisis.
Banks ran wild with unregulated markets that ended up being a huge percentage of the economy. That's what got us into trouble.
Banks and the financial sector were always heavily regulated, even during the years before the crisis.
The whole securitization of debt and cutting it up into tranches only get fuelled up to such an extent, because there were customers hungry for yield but barred from buying anything that didn't have some official (even useless) triple-AAA stamp on it.
Banks ran wild with unregulated markets that ended up being a huge percentage of the economy. That's what got us into trouble.