Comment by tomhoward
It's called "virtual interlining".
The startup I co-founded (Adioso - YC W09 [1]) tried to do it, including having discussions with a travel insurance provider about offering "layover protection" - so that if one leg was delayed causing you to miss your onward leg(s), your costs are covered. Kiwi.com does this now.
We worked on it from about 2008 till 2013 then basically gave up, as it was too hard to offer a service that customers could really love and trust. (It wasn't for nought; the technology we developed was valuable, and the company was able to rebrand and pivot and now does important work for airlines to optimise loads and fares [2], though I left when the rebrand/pivot happened).
The thing that makes it hard to do is it's basically impossible to get all the flight inventory, including fares and seat availability, that's complete and up-to-date enough to deliver a service that customers can trust.
The engineering challenge is one thing - solving a multi-dimensional travelling salesman problem (price and distance/duration) highly repetitively - but you can solve that with enough smart engineers and "compute", which ITA did in the early 2000s, and on a smaller scale, our team did a decade later.
But you could build the most beautiful routing engine the universe has ever seen, and still have a user experience that's kind-of garbage because the industry just keeps the flight inventory data so locked down.
These days there are APIs and feeds available from the major distribution platforms - Sabre, Amadeus and Travelport, but it's still not comprehensive. You often still need to negotiate individual agreements with major airlines in order to be able to publish and sell their fares. And even then, many of the low-cost airlines (which are often most of interest to travellers who want to find the cheapest route and deal with self-transfer) are not available through these distributors, and some, like South West, have blanket refused to be on 3rd party search sites, only starting to relax that position very recently and only with the dominant platform [3]. Kiwi.com has only recently come to a partnership agreement with RyanAir [4] after being in legal battle with them for years [5]. (I hate the thought of having to be at war with your most important partners).
Others have mentioned Skyscanner, which was always the closest to us in what we were each trying to offer (we talked briefly with them about being acquired by them).
Right from the beginning when we got funded for Adioso, my mind became fixated on the thought "if only you get every single flight in the world loaded into one big graph database, what could you do with it?", but it turned out to be a very big "if".
[1] https://techcrunch.com/2010/08/31/adioso/
[2] https://amadeus.com/en/blog/articles/creating-a-private-resa...
[3] https://techcrunch.com/2010/08/31/adioso/
[4] https://media.kiwi.com/company-news/kiwi-com-and-ryanair-ann...
[5] https://www.travolution.com/news/kiwi.com-celebrates-three-w...
Why would airlines even want penny pinching customers to snag the best deals via a third party?
At the very least it would make more sense to let their own frequent flyers snag such deals.