United Airlines employs 12712 pilots. [http://www.airlinepilotcentral.com/airlines/legacy/united_ai...]
United has 143 million passengers. [http://newsroom.united.com/corporate-fact-sheet]
If we say that United has a cost per pilot of $200,000 (likely high) then the cost per pilot per passenger is $17.77
You can probably also factor in a large component of overhead just managing 12,712 people. Scheduling, logistics, HR, etc, etc.
Even if you said it's in the range of $17-30 per passenger, that's pretty significant on many routes - particular high-volume short-haul.
You can also probably fit a dozen more seats on the plane.
That is not a small number.
$354 average domestic fair x 143M passengers = $50.6B in total fairs.
So $2.5B pilot cost is roughly 5% of their total costs. You can not lower gas costs nor airport costs nor plane costs much, but if you could eliminate $2.5B in salary, and add more flexibility, then yeah, I'd say there is massive incentive if the marketing and safety issues can be overcome.