The law not working for "minor cases" (which includes cases over hundreds of dollars) is exactly the failing of the justice system I mentioned. This isn't universal, in many places you can get theft of a Mars bar or possession of tiny amounts of drugs prosecuted very effectively, all cases much more minor than the typical credit card dispute.
So, rather than having a financial system with basic consumer protections (which would allow transaction reversals and contestation), you would prefer we have a criminal justice system which aggressively enforces and prosecutes minor offenses? I think there is a weak connection between the two, particularly since most situations where we do things like dispute a credit card charge are civil matters. And, as stated above, requiring civil suits for something like disputing a credit card charge is an enormous burden, and puts the burden on the consumer. (Which will also disproportionally affect the poor.)