The blockchain doesn't prevent a run on the "banks." If everyone decides to cash out at the same time out of fear of a crash then the currency crashes and there isn't enough money to liquidate everything (until it has no value). It isn't an improvement for that. If anything, it's a negative. Banks can implement policies to prevent it, but you can't really do so with crypto.
It would be useful for things like deeds and contracts. Instead of having a bank hold it and provide proof you could store it on the blockchain. There are a handful of good uses for it, but it's generally not useful for the stuff most people think it would be.