Searching actually does cost them money. Most airlines don't even have the ability to sell you a ticket without getting a third-party company involved (the GDS: Amadeus/Sabre/Travelport). The GDS charges the airlines money for every search to send their own data back to them.

I'd argue that's the root of the problem here.

That is not even close to the root of the problem.

Airlines could solve that problem themselves. And will the instant it’s actually worth it to them.

Airlines are being pressured to change the way they do their differential pricing, but the old system wasn’t some gold star land of virtue method either.

Surely that cost is still not the expensive part of the search?