By design TFA uses something one possesses that nobody else does, isn't this identical in principal as the private key?

I understand why and how this adds the extra security for the 'traditional' password authentication due to all the methods of compromising a password: brute force, guessing, exploits etc.; so for TFA to add an extra layer surely the private key would have to be exploitable in some form?

Maybe I phrased myself incorrectly in that I still see how it adds an extra layer of security but I fail to see why one would do this on top of a key based auth method.

I know the original article didn't mention using it on top of key auth but I wanted some insight as to whether or not it would be worth doing. As do many, I use TFA for any online service I can so I do appreciate its point in that sense.

EDIT: I never really considered the fact that the private key could be stolen via malicious software. Taking that into account I see the value in TFA for SSH.