A race to the bottom on pilot pay won't help anything. Well it may lead to less qualified pilots. You can ask Boeing how well screwing over labor has worked for them if you like.

All US airlines have the same labor costs for pilots and it isn't their highest cost anyway. That would be fuel.

If you want to divvy up costs that way: Boeing is probably the biggest problem. Both them and Airbus eat up all possible excess profit on the back end via the cost for airliners. Break up Boeing, bring back competition in airliner manufacturing. People who want to screw over labor don't usually frame things in those terms for some reason.

How exactly does Boeing drive up the cost? The cost of the aircraft is less than 20% of the lifetime cost of operating an airliner and a lot of the maintenance cost is not related to the cost of parts from Boeing, since most parts that get replaced on an aircraft are not made by Boeing and airlines do not go through Boeing to buy them.