> Eliminating any statistically significant difference between a high-quality human-written text and LLM-written text is exactly what the LLMs are being trained for.

I think you're basing this off a fundamental misunderstanding of what these detectors look for. LLMs generate human-like text, but they also generate roughly the same style and content every time for a given prompt, modulo some small amount of nondeterminism. In essence, they are a very predictable human. Ask Gemini or ChatGPT ten times in a row to write an essay about why AI is awesome, and it will probably strike about the same tone every single time, with similar syntax, idioms, etc.

This is what these tools detect: the default output of "hey ChatGPT, write me a school essay about X". This can be evaded with clever prompting to assume a different writing personality, but there's only so much evasion you can do without making the text weird in other ways.