The results of an LLM are an arbitrary approximation of what a human would expect to see as the results of a query. In other words, it correlates very well with human expectations and is very good at fooling you into believing it. But can it provide you with results that you disagree with?
And more importantly, can you trust these results scientifically?
But the real question is not whether you agree with the results, but whether they're useful. If you apply an objective method to data it is unsuitable for, it's garbage in, objective garbage out. Whether the method is suitable or not is not always something you can decide a priori, then you need to check.
And if trying it out shows that LLM-provided clusters are more useful than other methods, you should swallow your pride and accept that, even if you disagree on philosophical grounds. (Or it might show that the LLM has no idea what it's doing! Then you can feel good about yourself.)
I wonder, if well-educated and technically-literate people like him and you are willing to accept arbitrary results from a language model as a replacement for objective math, then what should we expect from the general public?
I'm not sure about ChatGPT, but I know Claude has a data exploration thing where you can upload a CSV and ask it questions; it generates Python code and it can be reviewed.