Could the PW1120 power a F-16 ?

Remember when GD were toying with the idea of a downgraded F-16 to replace the F-104s that was powered by a Phantom’s J-79 engine ?
Why didn’t they instead of the J-79 , offer the PW1120 instead?
As I remembered the PW1120 was lightweight but offered 20% more thrust than the J-79 . In theory , it could be shoehorned into a early viper without any problems . So GD could not be accused of offering a plane with outdated equipment nor can the US goverment accuse GD of selling their latest stuff to allies that may become their enimies in the future ie Iran