Inference alone is certainly profitable. I'm running models at home that are comparable to performance of paid models a year or so ago for free. Even for much larger models the cost around inference serving are clearly manageable.
Training is where the costs are, but I'm increasingly convinced those too could have costs dramatically reduced if necessary. Chinese companies like Moonshot.ai are doing fantastic work training frontier models for a fraction of the cost we're seeing from Anthropic/OpenAI.
This isn't like Uber or Doordash where the economics fundamentally don't make sense (referring to the early days of these services where rates were very cheap).
It's a compelling story that "current AI is unsustainable", but it doesn't pan out in practice for a multitude of reasons (not the least of which is that we can always fall back to what models did last year for basically free).