Except that in most "real" two-factor systems, you can't duplicate the second factor easily. The problem here is if the private key is in main memory, malware can copy it to another computer that will be indistinguishable (for the purposes of authentication) from the first. With something like a smartcard that is made much more difficult. Not impossible, but beyond the reach of most folks.
You have a point. I would like to see crypto chips on motherboards/in the CPU that can generate a key, export a public cert and then be asked to sign things. Then this vulnerability disappears.
This is 2 factor authentication... Validating something you have (ie the computer) and something you know(ie a password).