The "my train" convention is an interesting argument. It's not actually yours, you're buying a train-as-a-service single-use license, and there are tiers to that too.

I guess the main difference is that TAAS has many different trains where the experience varies wildly, so it helps to be specific on which train you're licensing; but LLMs are the same product for everyone, and you can't stay with say, ChatGPT 1.0, you get the same choices as everyone else.