[jlgaddis]

The SIM card in your phone is, basically, a smartcard. The private/public keypair on the SIM is how your phone authenticates to the cellular network.

Is what you're asking technically possible? Sure. What motivation do the cellular companies have to implement it, though? They are currently satisfied with the level of security already offered and to do what you are asking would cost a not-insignificant amount of money with little or no return (for them).