The problem is that if you take away the LLM, all of a sudden you can't do any of the things you "learned". It's confusing familiarity with understanding.
In your mind, is netcat also an API client? When normal people talk about api clients, they're referring to an sdk or a cli which provides a simpler interface for a specific API.
Making the model use curl is even stupider. It still needs to do the same amount of work to lookup and understand the API contracts (assuming those are even public). But now it also needs to juggle the auth flows and marshalling at the tool call level.
Even if your agent has internet access, why waste tokens having it re-discover and re-implement its own API client each time? It doesn't make any sense.