Too many chaps and chapettes are way to "Gotta to complete the mission oriented.".
Safety of operation comes first, regardless of what the toads sitting in their warm OCC offices say. I've been doing this commercial flying way too long to be intimidated by any of those sitting in their ivory towers.
If I realize that on time may not happen, I will request either a swap for a SLOT with a colleague or just request a revised SLOT itself. Once underway, there is no problem with asking for as many short cuts as possible, and cruising at a greater mach number to make up time. I know the 737 it does not really make a difference, but in the old 727 from .80 to 875 made a difference.
Bottom line... safety of operation comes first. All in the front must be comfortable with the operation. The guy or gal in the right seat must realize that the guy or gal in the right seat will put safety first.