The reason that bank runs and failures are so destructive is because of the state build cartel, driven by central banking. That was built in order to prevent competition and to let fractional reserve(which is in essence fraud) to run wild.
The only reliable way to ensure stability in banking is to separate it from the state and let the free market do what it does in every industry known to man, weed out stupidity and fraud.
And that's assuming people are rational and wise. They're not. For example since the Bitcoinia failure, the free market has lead to a whole bunch of Bitcoin users investing in something that has all the hallmarks of a ponzi scheme and accusing anyone who points this out of trolling and slandering the guy running it.
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.