The metaphor might be a bit esoteric, but that's similar to wishing that Hardware Security Modules (HSMs) allowed you "get your <private keys>" out of the HSM. As sibling comment says, that's how you get phished. The whole point of an HSM (and a passkey) is that the super-secret private part never leaves the HSM no matter how nicely you ask and no matter how compromised the machine is.
A password manager, OTOH, is happy to hand out your private key ("password" in this case) to anyone that has access to it.
It's a middle ground. You should be able to move passkeys from one vendor to another with some export process but the secret key is not exposed when you use it which reduces the risk of having it stolen
It's not that kind of impossible. It means that even if you are tricked into giving your passkey to the attacker, it's cryptographically useless to the attacker because a passkey is bound to a specific origin.
True, but it also opens me up to using the same password on all machines I use. You can argue that’s a negative, but personally I like being able to add a new machine to my collection without worrying about who the vendor is.
A password manager, OTOH, is happy to hand out your private key ("password" in this case) to anyone that has access to it.