The reason this particular quirk annoys me so much is that it isn't good writing advice.
Consider the two examples from this article (which may well have been human-written for all I know):
"These numbers come from OpenAI itself. There is no independent audit, no time series, no disclosed methodology, so we have no idea..."
No time series? That's non-sensical to me, it feels like that's there just to fill the quota of three things. Plus why would we assume an "independent audit" until told otherwise?
Then in the weird table, for "Institutional infrastructure" against "Personal AI safety":
"Scattered across psychology, HCI, education, and clinical informatics departments. No dedicated institute, no named fellowship, no equivalent job board."
Again, "no X" in a pattern or 3. And non-sensical - why would the fellowship be named?
It's word salad, there to fill a three-nos quota.
Yeah, no, I absolutely agree with you that TFA is not an examplar of good writing. But would just argue that the problem has little to do with these snowclone patterns or the rule of 3, and a lot more with the actual substance not fitting the form, and arguably not being substantive at all.
I'm all for rejecting bad writing and bad reasoning, but just wouldn't us as a community to get into the habit of rejecting otherwise good writing just because it's AI-ish.