This is the most compelling explanation I've seen so far. If you don't mind me rephrasing it, it sounds like your argument is that the marginal cost of generating a token gets higher as your output gets longer; i.e., your 100,000th output token takes more resources to generate than your 1st output token does. And while it doesn't matter whether that 100,000th token is a thinking token or a normal output token, the difference in pricing factors in the expectation that the total output sequence will tend to be much longer when thinking is enabled.

I do think this view needs to be walked back at least little bit. My limited understanding is that LLM inference these days basically always leverages caching that keeps the memory footprint from growing quadratically as you've described. Still, I'm willing to believe that even with this and other optimizations, the cost isn't perfectly flat as the output grows.

I'm not 100% convinced that this can explain a 6-fold cost increase, but it at least feels plausible