Selling inference for more than inference costs is not incompatible with bleeding cash at ungodly rates. They do in fact pay ungodly amounts of cash for other things, like training, marketing, etc. Heck, you can bleed cash while being profitable (in the accounting sense)

Also, API prices going up a lot every new version is more an OpenAI thing, and even there it's a recent trend: GPT 5.0 was a big price drop compared to 4.1, and 4.1 was cheaper than 4o, which itself got a price cut at some point and is cheaper than 4. Meanwhile Anthropic's API pricing stayed stable for many versions, then got slashed to a third with the 4.2 release and have stayed at that level since.

But explain to me how these companies will recoup these costs outside of increasing inference pricing?

Their business model is selling inference but the training and other costs have to be accounted for somehow. Unless I'm missing something obvious, inference costs must go up drastically if these companies are going to survive beyond the subsidy stage.

Sell more. The hope is that there is a huge addressable market that includes huge per-worker demand in almost all white collar work and lots of inference in people's private lives

If that doesn't work, then yes, then prices will have to go up