For Claude specifically, (1) enterprises pay API rates on top of subscriptions, so subscriptions profitability questions are only relevant for smaller companies and indie devs. Many of whom probably have sporadic or low usage which helps balance some heavy users.

Again, for Claude, (2) it’s rumored that their API rates have around a 90% profit margin. It’s also claimed that the subscription limits get you around 10x tokens per monthly dollar vs buying them with API rates.

Edit: to drive it home. If a tokens true cost to anthropic is 1/10 of what they sell it for at API rates, and a subscription gets you tokens at 1/10 the price, that’s cost-neutral for the business if every subscription uses every token. They’re selling tokens at cost, not at a loss. Many subscription users won’t use their full allotment. That means serving some users doesn’t cost the business as much - which might push the subscription business from cost neutral to profitable.

What's the basis for the opposite?

I think theyre charging at least 3x marginal cost for the api and I think that the average subscription uses around half its token allotment. So subscription needs to give 6x as many tokens as the api would cost for it to break even for the lab and that's around where they tend to sit