The issue is that an API is kinda the foundation of everything. It's really hard to have that foundation when it could just decide not to be that foundation because one of the values in your POST request contained a text string that caused it to hallucinate.
LLMs can only process raw text, and any version of one that can run fast enough to replace a REST api will either have to be baked into bare metal and every API update now requires months of retraining on a test suite then fabrication of new chips, or you use a general purpose one with 1000X the compute.
This whole system still requires you to build an API that it can be tested/trained with anyways, and it will end up dispatching requests to that base API.
Why even have the middle man at that point? Just document your API and be done with it...
