“Does Reb Dovid permit use of a timer on Shabbos for an air conditioner, even though he’s father forbade it?”
No.
“Why does “the velt” that generally follows Reb Moshe’s psakim disregard Reb Moshe when it comes to air conditioners on a Shabbos clock?”
Halacha is largely determined by consensus. the “velt” was never mekabel this pesak. As DY points out I don’t think many people follow alll of R’ Moshe’s Pesakim. I was at a wedding that R’ Bluth attended, at which he left early. My father jokingly asked him if he made sheva berachos at his table which R’ Moshe holds is a chiyuv on individuals at a wedding. I dont remeber his reply but he didnt