Are OpenAI and Anthropic losing money on inference?

This seems very very far off. From the latest reports, anthropic has a gross margin of 60%. It came out in their latest fundraising story. From that one The Information report, it estimated OpenAI's GM to be 50% including free users. These are gross margins so any amortization or model training cost would likely come after this.

Then, today almost every lab uses methods like speculative decoding and caching which reduce the cost and speed up things significantly.

The input numbers are far off. The assumption is 37B of active parameters. Sonnet 4 is supposedly a 100B-200B param model. Opus is about 2T params. Both of them (even if we assume MoE) wont have exactly these number of output params. Then there is a cost to hosting and activating params at inference time. (the article kind of assumes it would be the same constant 37B params).

Gross margins also don't tell the whole story, we don't know how much Azure and Amazon charge for the infrastructure and we have reasons to believe they are selling it at a massive discount (Microsoft definitely does that, as follows from their agreement with OpenAI). They get the model, OpenAI gets discounted infra.