I worked for an OTA (currently a brand owned by Expedia, like most of them, but a real company back then) and we always had issues with airline bookings, as the airlines did not want to expose all of their offerings to us so they could make extra money later. We always got yelled at by people who booked Spirit, as their "price" in our system was always the lowest, but after booking, the airline would add on fees for so many things that the flight was no longer cheap, but it was somehow our fault.

Airlines also give up almost no commission to anyone, local travel agencies or online, so it's generally profitless to book them for someone other than hoping you get to book a hotel as well, which is negotiated to provide profit. Airlines also hate comparison shopping; they want you to book on their website so you can't see what someone else might charge for the same flight. Southwest was/is the king of that; they allowed no sales elsewhere, so you could never tell if they were cheaper/cost more. It's like insisting that a monopoly view on prices is best for the customer.