"Haha I used the API which I KNOW is governed by the ToS but I didn't agree to it"
Judge: "do you agree to the terms?"
"No"
Judge: "then you can't use the API"
"But look at all the downvotes this is getting! You're wrong Mr. Judge!"
Judge: "do you agree to the terms?"
"No"
Judge: "then you can't use the API"
"But look at all the downvotes this is getting! You're wrong Mr. Judge!"
That is the purpose of public APIs. Usage without prior agreements.
If the API providers want to restrict the usage of their APIs, they are free to make them non-public.