But sites that have been doing that have existed long before LLMs and AI agents. Google Flight is a good example. You see comprehensive price comparison across different airlines, click the cheapest and book it through airline website. How is this different?
Enough people use Google flights that not being there is worse than being there. But if airlines had their way, not even that would be a available. I've looked into building my own flight search engine once, and (official) access to that data (ie not scraping) is very hard and expensive to get, to the point of being pretty much impossible if you're not a huge corporation.