That is one reason given, but apparently, this method still is deemed appropriate by rabbis in foreign countries, where their food is just as processed as it is here. How did and why did the Rashba’s shita become de rigueur? Why does nobody hold like the Noda be Yehuda here these days (except Rav Abadi and maybe a few others)? Largely in America, this is irrelevant, since I’d say that at least 70-80% of processed food items have some kind of a hechsher (whether it be one of the Big Five, a K that actually has rabbinical supervision behind it, such as R’ Greenblatt on hot sauce, or R’ Zevulun Charlop on Starbuck’s drinks, or R’ Goldsmith on Royal gelatin, or a hechsher that is less respected by the olam, such as the Luchot K, UKS, Triangle K, etc.)
If you hold like the OP or like Rav Abadi that cheeses made with an automated system aren’t gevinat akum, than that would obviously open the floodgates.