Public keys are published that's the basis of any asymmetric encryption algorithm, on ethereum, bitcoin you are publishing a signed message that means you are also emitting your public otherwise how one can verify that you signed the tx. Regarding Quantum computing i wouldn't be so sure knowing that we can see a quantum computer with 1500 QBIT starting from 2028, this will be sufficient to crack any bitcoin wallet in less than 10minutes. As you mentioned the current hurdles are the huge error rate but dont be fooled that its going to be that way, even modern computing used to have this kind of errors (not the same nature but still errors) in the beginning...