I don't think that's clear. They're certainly burning money, but that's mostly R&D: salaries and training compute. Once you remove those, it's unclear whether the AI companies would be losing money on just inference.
You can't "remove" costs willy nilly to make a company look profitable. Running an independent ISP is an extremely lucrative business if you gloss over the capex requirements of installing and maintaining the infrastructure.
You don't remove them willy-nilly, but evaluating companies based on their operating costs is standard accounting practice. R&D is not part of operating costs.
Capex for inference is in, capex for training is out for that analysis.
It's one of the key metrics of a business. These are growth businesses, everybody assumes they're going to have a lot more customers in the future than they have today.
If they've got X times as many customers next year than they have right now, training costs per customer gets divided by X, but inference costs per customer stay roughly constant.
So for businesses where they expect X to be large, they care about operating costs a heck of a lot more than R&D.
There was some credible analysis that I don't have the link to which estimated 50% gross margins for OpenAI, largely eaten up by operational expenses. So not awful unit economics, but not good either.
Assuming that's even true, the big asterisk is uncertainty around efficiency gains in the future. The intelligence divided by cost ratio is changing very quickly. It is hard to make confident predictions more than 3 months out.