1. Reb Moshe was not mechadesh the heter. It was an accepted psak before he arrived. Rabbonim were meikel, albeit never wrote Teshuvos.
2. Rav Henkin, the Chazon Ish, Reb Aaron Kotler, and Reb Eliezer Silver all held it was muttar. These were basically the greatest Poskim America had at the time.
I heard from a chosheve rav that if you look through the tshuva from R Moshe you will see the reason why he bent backwards to find a heter is because of the issue that there were Rabonim in America at the time who were meikel. He said that it seems like R Moshe was almost "forced" to find a heter because if he didn't find one then the people asking the question would say 'if what my rabbi says about kashrus (Cholov Stam) is worthless then what he says about taharas hamishpaha and shabbos must be nonsense also'
For example, say the חזו״א says one can be somech on the פרי חדש (need to check on that), that’s a significant point to take into account להלכה.
I have heard that the old editions of חזו״א says one can be somech on the פרי חדש however in the newer editions it has been removed. Either way it has nothing to do with the hetter from R Moshe, and if one in America is somech on R Moshe it would not allow them rely on R Tzvi Pesach Frank which relies on the פרי חדש. Therefor they cannot eat non-mehadrin dairy products in Israel which say on the Avkas Cholov Nachri.