Many of the companies (including OpenAI) have even claimed the opposite. Inference is profitable; it's R&D and training that's not.
And TPUs are like 5x cheaper then GPUs, per token
Inference is very much profitable
We can't pinpoint the exact dollar amount OpenAI categorically spends but we can make a lot of reasonable and safe guesses, and all signs points to inference hosting being a profitable venture by itself, with training profitability being less certain or being a pursuit of a winner-takes-all strategy.