Agreed. Not that the two were called competing against each other, but imagine if the F-20 had been picked instead of the F-16. There is no way the smaller F-20 would be able to carry all the stuff the F-16 has.
Don't get me wrong the T-38/F-5 airframe is very capable and nimble. But, like you said, it's a 1950's design that had already maxed out it's growth potential.
It is a tribute to the F-16/F-17 design teams that their respective planes evolved into domineering 4th generation fighters.