The question I have: how much are they _also_ losing on per-token billing?

From what I understand, they make money per-token billing. Not enough for how much it costs to train, not accounting for marketing, subscription services, and research for new models, but if they are used, they lose less money.

Finance 101 tldr explanation: The contribution margin (= price per token -variable cost per token ) this is positive

Profit (= contribution margin x cuantity- fix cost)