1) You're wasting GPT tokens on outputting JSON instead of meaningful information.
2) GPT functions won't, with absolute, 100% certainty, return JSON in the schema you want. In 1% to 3% of cases it hallucinates fields, etc.
3) This also allows you to output data in arbitrary non-JSON formats.
4) You can't self-host OpenAI functions.
As with the other poster, I’d be interested to hear a bit more about point 1.
I think what factors in even more when you use the API is that you do not have fine-grained control over the generation process. If you follow the MS guidance approach, you fill in structured text yourself, and then let the model generate only the value parts, e.g. up to the next quote. To do that more or less word by word, you have multiple API calls, and have to be very smart about providing the right stop tokens.
Does this help clarify?