It depends a lot on which LLMs you're talking about, and what kind of usage. See e.g. the recent post about how "Anthropic is bleeding out": https://news.ycombinator.com/item?id=44534291
Ignore the hype in the headline, the point is that there's good evidence that inference in many circumstances isn't profitable.
So he's using their API prices as a proxy for token costs, doesn't actually know the actual inference prices, and ... that's your "good evidence?" This big sentence with all these "We don't knows?"
Does this idea upset you for some reason? Other people have analyzed this and come to similar conclusions, I just picked that one because it's the most recent example I've seen.
Feel free to look to a source that explains how LLM Internet is mostly profitable at this point, taking training costs into account. But I suspect you might have a hard time finding evidence of that.