Google Flights, ITA Matrix and all similar public search tools go to great lengths to prevent any kind of bot from accessing them -- any attempt to access the underlying API will result in being blocked after only a few queries, and even coming through the "front door" (the official UI) there are strict rate limits. This is why things like Power Tools for Matrix have to be implemented as a plugin / user script inside the browser, so that it's still a normal web browser accessing the tool in the normal way. We consumers are effectively denied the possibility of a free competitive marketplace of flight search tools due to the fare data being proprietary.

Computer use (for this use case, the LLM would automate a web browser to use Google Flights / ITA / etc) is a decent workaround and is a very active field of research at the moment with Anthropic and OpenAI both having early versions of it.