For proper 2nd factors the secret is a hardware key that practically can not be extracted so it is impossible for someone to know it. They must obtain the piece of hardware to use the key.
Yes, that is certainly a more secure second factor since there are fewer ways for an attacker to steal it, but I don't think that should be a necessary condition for it to be called a second factor at all.
Can't say I agree with this take. Sure, something hardware bound is more secure under certain threat models. For others it's largely irrelevant. There are also drawbacks, such as not being able to back it up. That might or might not matter. "Just" get a second hardware token, register that as well, and store it somewhere safe won't always be a realistic (or perhaps desirable) option for everyone in every scenario. It certainly reduces your flexibility.