Lots of businesses have subscription programs in which a small number of users are money losers, but which in aggregate make money.
It's not even obvious that the labs are losing a lot of money on even a minority of users; the rate use caps are fairly aggressive for Anthropic, and a cursory analysis of likely actual cost of serving tokens shows they are high margin products at the API level and unlikely to be unprofitable within the usage constraints provided to subscribers.
I do think subscription models make commercial sense because users want predictable costs, and it's a club good in which marginal token cost is zero which helps consolidate their customers' purchasing volume to one provider. But that's a different claim than them serving it unprofitably to kill competition.
Also, they (Anthropic) are transitioning many of their enterprise customers to API consumption billing anyway.