The indication that OpenAI's inference is profitable is that 3rd party providers host large models for cheaper.

Given that OpenAI is ahead in intelligence, it's also reasonably likely that they are at the frontier of efficiency too.

Your "evidence" for OpenAI's inference not being profitable is apparently based on leaked financials supposedly showing growing losses for reasons entirely unknown.

With their research, training, data centers, chip development, and hardware product development, there seem to be a number of reasons that might explain growing losses.