I wouldn't. Why can't you use banks that agree to follow rules you like and be monitored by people you trust while I can use banks that agree to follow rules I like and be monitored by people I trust?
There are 2 reasons.
The first is because ultimately you rely on the state's monopoly on legitimate violence to enforce those rules. If you want protection from fraud or simply outright theft, you need to rely on the mechanism of the state. And the state might determine that a contract or transaction, though voluntarily entered into by both parties, is still unenforceable because it unconscionable or harms the general welfare.
The other reason is the experience of the Great Depression, where for instance over 5000 banks failed in the US prior to the creation of deposit insurance. People making prudent decisions in good faith can still collectively make a system unstable. And if you lose you savings that's a problem for you, but it a few million people lose their savings that becomes a problem for society.
Obviously that is a simplification, but it shows why letting each customer choose for themselves how unregulated their bank should be is recipe for disaster.
A common set of rules across all banks ensures that they'll continue to work with one another.