> We are paying for a certain amount of token consumption
I dont think you are. The specific arrangement you have is you pay for a subscription to be used with Claude Code. It isnt access to tokens, so you can do whatever you please.
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An analogy would be a refillable cup for a soda at a restuarnt. They will allow you to refill how many ever times you want, but only using the store provided cup - and you cant bring your own 2L hydroflask or whatever. You're paying not just for the liquid, but for the entire setup.