They are obviously losing money on training. I think they are selling inference for less than what it costs to serve these tokens.

That really matters. If they are making a margin on inference they could conceivably break even no matter how expensive training is, provided they sign up enough paying customers.

If they lose money on every paying customer then building great products that customers want to pay for them will just make their financial situation worse.

By now, model lifetime inference compute is >10x model training compute, for mainstream models. Further amortized by things like base model reuse.