You didn't lose your entire savings if you lost your wallet, usually.
Quickly you end up in a situation that either starts to look like how financial companies keep their most high risk keys, or end up outsourcing the whole thing to something that quickly starts to resemble your bank.
So ultimately it's just like cash: Fine for small amounts. Risky, but maybe livable for somewhat larger accounts, or a giant headache that will probably bite you when you start looking at lifetime savings.