I imagine a lot of people want to make sites like this, but they don't have the resources to obtain contracts for data feeds.
Much like many people would like to open up streaming sites for Big Label music, but not everybody can afford to enter into contracts with music labels then have hundreds of HDs full of wav files delivered to them.
We need someone to make a pay-per-taste brokered data market.
Basically, getting the raw data is quite difficult, but once you have it, you need to expend a really enormous quantity of engineering work into using that data to get useful answers.
For example, ITA invented a language to describe taxes. That's because the tax code changes all the time and is incredibly complex. There are fares which different entities in the airline industry price differently due to tax code ambiguities. The search problem is really very hard once you have the data.
Now, ITA software does offer their flight search engine as a service: you sign a contract with them and issue queries and they send you responses. I don't know how interested they are in cutting deals with really tiny startups, but they might be amenable. You will of course have to pay in some fashion: maybe a fixed fee per query or pay per compute time or pay per successful booking.
At the time I left the travel agency in question, Galileo was in the process of rolling out a new version of the API, but the few times I tried to get it to work, it seemed completely broken (this was for cruises, not flights, but it was the same general idea).