And if Estline was indeed putting either implicit or explicit pressure on the captain (and crew) to adhere rigidly to operating schedules regardless of negative externalities, then 1) I would fully expect the JAIC investigation to have uncovered this and listed it as a salient factor within the report, and 2) there would have been legal/civil ramifications for Estline as a result.
In the aircraft industry, it took a very long time to convince airlines and flight crews to abandon the twin evils of "get-home-itis" and rigid adherence to company logistics and efficiency goals. As so often, it took calamitous outcomes to act as a driver of change. Perhaps the most vivid (and certainly the most disastrous) example was the Tenerife double-747 accident in (IIRC) 1977, when a confluence of factors led to such long delays that the Dutch KLM captain realised that he and his crew would surpass the then legal limit on continuous hours of work - this would have meant that the aircraft (and all its passengers) would have had to sit parked up at the gate until KLM could fly in another flight crew. That would have resulted in very unhappy passengers, expenses associated with putting up the passengers in a hotel and flying in the new crew, and disrupting KLM's aircraft logistics (again IIRC, that aircraft had been due to depart Amsterdam for New York first thing the following morning, and KLM would have had to find a replacement 747 if the intended aircraft was stranded in Tenerife until the following morning. And all of that would have reflected badly upon the flight crew aboard the Tenerife aircraft.
So the KLM captain (who was also a somewhat arrogant and entitled "star" in the airline - another salient factor) was hugely impatient to get in the air and get back home before they ran out of hours. There's no doubt that this played a major role in the ensuing disaster: the KLM 747 started its take-off roll down a fog-bound runway, without proper ATC clearance, and it slammed into a PanAm 747 that had been taxiing in the opposite direction half way down the runway.
As a consequence of this hideous disaster (which remains the single worst loss of life from an air accident in history) and several other fatal crashes (including at least three where captains were so dead-set on touching down at their intended destination that they took disastrous risks in order to (try to) do so, instead of diverting to an alternate), the airline industry gradually realised - and had it forced upon them in several FAA rulings - that safety is always the number one concern; that captains should be expected to use their experience and discretion to judge even the slightest risk to safety and modify flight plans accordingly; and that airlines should allow for such actions without repercussions, and they should budget accordingly as well.
I now return you to your regular programming.