The competitors of a bank practicing fractional reserve and cargo-cult security would have a major incentive in pointing that out, in order to gain market share.
The free market does not lead people to nothing. What 'it' does is to reward lucrative (i.e. economical and profitable) behavior and to punish stupid ones. It is a form of social organization with an embedded stabilizing mechanism.
The same could be said of centralized banking, or centralized anything, as could be more easily seen on the more socialist economies of the soviet block.
Given that, let the people invest their money as they see fit, and punish fraud (including fractional reserve banking) as the crime it is. Simple solution.