Earlier quoted context omitted.
Imagine you have 2 sets of keys to your house and if you lose both then your house is not yours anymore. That's what keeping your money outside an exchange seems like to me. Exchanges are easy and familiar to people. If there was some secure way to do password recovery that was built into the currency that might be a game changer. That might be impossible by definition, not sure.
I think you definitively could make something like Keybase on Bitcoin, by using multiple third-party institutions (chosen by the user) as a fallback. When sending coins to your storage address, you'd say "anyone can use this money if they have this private key OR if they get a digitally-signed certificate from 3 out of 4 of these keys (A, B, C, D)". Those keys could belong to different institutions (or persons) that…
Instead of doing what you suggested, normally it's 2 of 3 where it's your cold wallet, your hot wallet, and the online wallet provider.