If someone like Mystate goes broke well then that’s a minor adjustment to the federal budget to pay out the depositors. If CBA, NAB etc went bust then in practice it’s going to be rather hard for government to come up with the money at least in a prompt manner.
Also companies like BHP aren’t going to become worthless in a hurry. Even in a major crash their value isn’t going to zero at least not overnight. You might find you can’t sell the shares or at least not for a decent price but there’s still a real business there, there’s still real physical assets that can’t possibly simply disappear into thin air (unlike financial companies where that is indeed possible), and your share of it will have value at some point.