I feel icky replying in favor of a for-profit entity, but here goes ..
> 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.
The analogy is bad. Anthropic does not let you "refill however many times you want", they have limits. That's what "limits" in your account is.
It would be like the restaurant saying "you can buy the 2-liter soda pack" and then getting all uppity when you bring your own 2L hydroflask in.