It would be insane, if they can't serve the models at a profit sure at current GPU prices the profit might be 10% or lower. But at realistic gpu prices it would have been close to 30-60% based on how big the models actually are and how much they have optimized the stack to serve them.
1T parameter models like Kimi K2.6 can be served for 1/10 to 1/5 of the price of opus 4.8 for perspective.
Sure opus is 2x the size and hosting might be non linearly scaling so still it should be around 50% margin at regular gpu prices.
If it isn't I would be very surprised.
Also for enterprises we joke but Google is not paying same rates as us there are big massive enterprise discounts. I have heard upto 20-30%... OpenAI is supposedly even more generous.
I don't think API is being sold at a loss at the end of the day even if the API profits are marginal 10-20% because of insane GPU prices now.