You can get an arbitrarily low false positive rate by sacrificing against false negatives. It's trivial to make it zero, just classify everything as human-generated. Meanwhile a false negative rate of even 1% is a pretty big problem since someone can easily use LLMs to generate 100x the volume of text and then use whichever ones make it through the classifier.
And that's before anyone even tries to get the LLM to generate a different style of text. Or for that matter creates a "style model" that rephrases text.
You don't really need a style model - current models are very good at doing "style transfer" of a model text onto whatever it has written if you just have it do it chunk by chunk. It takes more to prevent it from being detectable by good detectors, but it does remove a lot of the worst tells.
The point being that you wouldn't need the developers of the most popular models to themselves be trying to fool classifiers because their output could be run through an independent special purpose one designed to remove the tells the classifier is looking for, and the special purpose one wouldn't need to be made by anyone with the resources to create a good general-purpose model since it only has to do that one thing.
My point is that you don't need a special purpose one to achieve this.