I've heard that the API calls by themselves are ~60% profit if you ignore capital expenditures. The labs haven't generated profit because they're constantly sinking money into the next generation of larger models to stay relevant. Dario has talked about the economics of this a lot, and I do believe him there.
There's clearly also a lot of pent up demand in the corporate world for inference, the problem is that it's currently expensive enough that enterprises are balking at the cost before they've had a chance to refine processes and see projects through to fruition. That's a tractable problem to solve though.
The number of capital-heavy businesses that are wildly profitable “if you ignore capital expenses” is too many to list.
Airlines, for example, which are so profitable they continually go bankrupt.
That's true, but if the frontier doesn't advance there's no depreciation or ongoing capital expenditure. If all the frontier labs agreed to stop making stronger AI and just try to sell what they've already trained today, their books would turn green in a hurry.