Most clients don't. It would fix a lot if they did, though. You'd still have to guard the root key with your life. If you lost a child key you could potentially recover by emitting a "move" event from the root key.

The clients should remain dumb to this process to avoid a leak. The users should be deriving the nostr key from their master key that they have thoroughly backed up in steel plates. You can recover the child key as long as you have the master key back up and the index number attached to the child key. This is primarily a security feature that users must warp their heads around. It has to be done in a secure environment, on a laptop that has never been online and that will never be online, with WiFi/BT and hard drive stripped and by using tails from a USB stick. Clients can't do this in a secure manner.