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.
Yes, you can store money at your place and then the burglars might get into your home and steal it.
I don't think that home is safer than bank when we talk about money. Besides, your savings in bank is secured.
In a.type of world that we live it's not yet possible to live without banks. Yes, a few xan, but these are people without regular income that have no need for credit cards or loans, bank account and similar and they usualy live very modest. But in general, for average citizen that would be very hard.