If it wasn't the case, the Claude API pricing would be the same, $200 for unlimited use. But it's metered.
We don't know if Claude Code bleeds money for every user that touches it. Probably not. But the different pricing is a strong enough clue that it's an appeal product with subsidized tokens consumption.
API is intended for a different audience - companies with a big pocket who aren't as price sensitive as private users. So the pricing will be different than for a private subscription.
There is huge value in getting people to subscribe to recurring payments. Giving people a discount to do so makes sense and does not mean that the subscription service loses money.
We don't know if Claude Code bleeds money for every user that touches it. Probably not. But the different pricing is a strong enough clue that it's an appeal product with subsidized tokens consumption.