Get-there-itis is absolutely a thing. No big airline would be dumb enough to say it that stuff explicitly but the pressures still exist.

There have been accidents around the world where pilots were trying to save fuel, get off work at a normal time instead of 2 hours extra holding, not wanting to divert and not be home, try to get on the ground so they don’t go over their max hours for the day, etc.

Yes it’s counterproductive. *It happens*. External or internal, it happens.