Are OpenAI and Anthropic losing money on inference?

"Why would you reinvest profits back into a business that is extremely profitable, when you have the chance of pulling your money out?"

You are making a joke but reasonably speaking there are a ton of software companies where they kept reinvesting where they should have taken out profit, especially when they are peaking.

Sure. There are times to pull money out and there are times to reinvest money. It's not always clear what the better choice is, except in hindsight. But parent poster was treating it completely implausible that someone would choose to reinvest profits back into a profitable business.