It is advisable to always have your savings at your place, not trusting the banks or anyone else. Because in which case, you have the opportunity to lose all your money, and literally stay with nothing. But in what exactly to store, everyone already decides for himself.
It depends really. Fiat is not the same as bitcoin where you could manage it yourself as long as you can secure your own wallet, and most of the people say that it is better to take care of your bitcoins than putting it in an exchange since you could consider that bitcoin not yours at all. Banks could give interests and not all of the people could save their money by themselves, another thing is that people always take loans to banks. That is the reason why I think people can't leave without banks.