You misread the flow:
Maybe the opposite = Today, he would Rav Moshe would ….
I was totally making it up. To show that it’s all conjecture what Rav Moshe would say.
You have quoted that same line from the Flatbush Teshuva multiple times. I read it differently.
This is really all boiling down to meta halacha.
It’s pretty clear to me what Rav Moshe’s deep reservations were.
Even if the mattirim had their opinions about Rav Moshe, there was still Rav Dovid in living flesh.
Alas, that didn’t become a factor.
It’s surprising to me that people will get all hot under the collar about the matirim not being given the prerogative to issue their own psak, yet are not bothered by the fact that Rav Dovid was unusually vocal and was ignored.