text-generation-webui offers an OpenAI API implementation, specifically to support OpenAI API clients, so you can get something more than just OpenAI support by just wrapping the OpenAI API.
You could have more flexibility by abstracting out the underlying LLM APIs, but then you also have a bigger deal with supported features of different APIs, the same conceptual feature supported with very different parameter structures, etc., etc.
You could have more flexibility by abstracting out the underlying LLM APIs, but then you also have a bigger deal with supported features of different APIs, the same conceptual feature supported with very different parameter structures, etc., etc.