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.
If something goes wrong it's cumbersome and agonizing enough to deal with the airline.
You won't, however, be hung out to dry by two entities wanting nothing to do with you and sticking their fingers into their ears going LALALA! at the top of their voice and shifting responsibility to each other.
This was (and is) different with physical travel agents who will support you, if necessary, but OTAs? No thanks! Forget it! Never, when it comes to booking flights.