The economics for daily use of inference seem to make sense. The cost of inference is highly profitable. The margins on inference around 80%. The lost money from power users is made up but the average user who doesn't user their tokens. They lose money on the free inference given away but that's marketing and getting used to people having the product there as a crutch. It's not the best business model but they can change it at any time and have vc cash to burn.
What doesn't make sense is recouping the investment cost of model training and building new data centers. Because the moat on a new model doesn't last long enough to recover its training cost.