No, I understand what you're saying, I just think you're wrong. To be a little clearer: you're assuming a single near-omnipotent agent randomly selects an anti-goal and is capable of achieving it. If we instead create 100 near-omnipotent agents odds are that the majority will be smart enough to recognize that they have to cooperate to achieve any goals at all. Even if the majority have selected anti-goals, it's likely that the majority of the anti-goals will be at cross-purposes. You'll also have a paperclip minimizer, for example. Now, the minimizers are a little scary but these are thought experiments and the goals will not be so simple (nor do I think it would be obvious to anyone including the AIs which ones have selected which goals.) The AIs will have to be liars if they select anti-goals, and they will have to not only lie to us but lie to each other, which makes coordination very hard bordering on impossible.

In some ways this is a lot like Bitcoin, in that people think that with enough math and science expertise you can just reason your way out of social problems. And you can, to an extent, but not if you're fighting an organized social adversary that is collectively smarter than you. 7 billion humans is a superintelligence and it's a high bar to be smarter than that.