ID checks are possible for first-party harnesses...but they would also mean no more API access. Your wrapper could easily become a way for a foreign national to query Fable. Maybe a few large customers like Cursor would work with Anthropic to prove they had implemented ID checks themselves as well in their own products, but being able to just get an API key and have your product call frontier models may be over.
First party makes no difference, an API can be created for any website or desktop application and served over a network to anyone. It just takes more effort.