1. If in your use-case it's important to let the user recover from lost keys, you can have some multisignature recovery (I designate n trusted parties like friends, family, governments etc, if I lose my key they are allowed to together designate some new address as me, and I trust them to verify me offline if I lose my key; we can do m-of-n multisignature, letting me trade of risk of them colluding to falsely verify someone vs risk of them not verifying me; using secret-sharing we can do this off-chain too).

2. If my use-case requires me to give someone access to my data in order to do their job (eg a hospital needs to see my medical records), then I think it's mathematically impossible to defend against what you said. (barring unlikely advances in homomorphic encryption and the like). Using public-key crypto allows us to eliminate having a intermediary party and the risk that the intermediary party gets hacked. Blockchain then allows us to credibly prove that our data existed at a certain point in time. Also there are use-cases where I maybe need not disclose all my data (eg maybe for some use-case my bank does not need to have access to my payslip, just a proof signed by my employer that it exists)