It is hard to say as there any things depending from banks, not just money keeping... and there are also a lot of people to whom it will be difficult to enter the crypto world for several reasons, mainly age and lack of base infrastruture...
But I think that if an event would terminate all the banks, the world would not go into the dark ages, it would jump ahead to a fully digital economy... at this point we don't really need banks because we have crypto... and after an adjustment phase I bet we would do a lot better managing our own finances and not paying those blood suckers