3. We don't want to call unwanted attention to the amount of power that Orthodox Kashrus organizations wield on a national/international level. This may be his most convincing argument.
With great power comes great responsibility. Championing this cause could end up hurting a Kashrus organization if other companies under supervision or considering supervision end up getting another Kosher symbol (or to be extreme, going uncertified) because they don’t appreciate that the agency takes action when it comes to things beyond what they’re certifying.
Remember after the Agri raid leftist orthodoxy tried to push for Kashrus agencies that certified other aspects of a company not just limited to “Kosher dietary concerns”, Tav HaYosher and the like, it’s likely a good thing such an initiative didn’t take off. Kashrus has enough politics as it is even without mixing in any of that potentially messy stuff.