banks are regulated to ensure they don't over-commit and are backed by a central bank to bail them out. That system isn't perfect, but it's a lot better then no regulation.

An unregulated system that allows fractional reserve banking can only end badly. Competition will cause private entities to take increasingly risky positions (if they don't play along, they get crowded out by those who do), and the systemic risk is unchecked. At its extreme, it becomes a ponzi scheme.