The recovery mechanism isn't intended to recover "lost" keys. If you still have your owner key and lose the other ones, you can use your owner key to set new values of the other key (that's what the owner key is for), so there's no need for a recovery mechanism for that.

The recovery mechanism is about "account recovery". Its useful in cases where someone else obtains your owner key and takes over your account with it, replacing your original owner key with their own.

In this case, you can show that you still have the "original" owner key and if you can somehow prove to the recovery agent that you are the "original" owner, then they can allow you to take back your account from the person that stole it.

A typical mechanism for this is you give your recovery agent an email address that they can verify your identity against. Or, if they know you in real life, you could make a video call with them or something to verify your identity.