“Can’t the hashgacha agencies (i.e. OU-D, OK-D) effectively replace whatever the inspections the FDA did in Rav Moshe’s time that they no longer do?”
The vast majority of milk changes hands from the farmer to the milking company. The company takes in milk from many different farms. One company I spoke with told me 700 farms. The company gets all the raw milk, pasteurizes it, homogenizes it, and then bottles it. This would present a big problem for any kashrut inspector; even C”Y can’t come from this system. To get C”Y one needs to have a dairy farm that goes all the way from milking to bottling in the same facility.
Besides that logistical problem, the average farmer would probably not appreciate an uninvited stranger coming to oversee his farm.