> Third party apps are not allowed by airlines to charge less than the airline

Technically true in that they can't undercut the airline on the same fare class.

But there are many different fare classes and some of them are only offered via 3rd parties, so you can often get much better deals via e.g., Expedia than you can by going direct to the airline.

Just this year my family flew Melbourne-Madrid then Milan-Melbourne, both legs on Cathay, but this route was only available on Expedia (and maybe other OTAs too, I don't remember) - all I know was that it was impossible to even search for this route on Cathay's own website. We didn't have any issues, but if we did I don't know if I'd worry about Expedia's customer service being much worse than an airline's own service.