How do you profit of a company that hemorrhages a few billion a year?

While it runs a deficit you don't or at least only through increased valuations, which ofc assume that you'll eventually be able to turn a profit. Will this ever happen for OpenAI, i have no idea, but that is the bet. And for the likes of Microsoft spending a few billions on bets like this isn't that big of a deal, just look at how much Meta burns in their VR department.

Even Amazon had AWS, which was the absurdly profitable core business at the center of a cost bleeding distribution center.

Uber was running a deficit for a long time until it turned profitable. It's pretty normal for many new companies to burn money first before they turn a profit. The biggest cost seems to be training new models constantly, and i assume one hope is that eventually this slows down. Then they need to get operating costs down that where i think they currently roughly break even (?) or maybe run a minor loss, but that seems doable, considering the pace at which hardware is still improving.

OpenAI is doing nothing to generate economic value.

I wouldn't say that it is nothing, but at this very moment it probably doesn't equal the immense amount of resources poured into it. That said, if things improve both in terms of the quality of responses you can get from models as well as reduced costs to run them, then there is definitely huge economic potential.

Point well made. Engineers, however quantitative they may be, are not often finance people. If the true believers were left in charge, they'd probably bankrupt promises much more rapidly, and auger the whole enterprise into the ground that much quicker. I can't see that Altman is actually that great a finance guy either, at least in stewardship of other people's money, but he has cultivated the ability to manipulate cash out of people and institutions during this grift-dominant era of Silicon Valley.