There is a balance, certainly. Flying a plane that I have financial responsibility over, I do care more about cost, but I tend to factor that more into which airports I land at, operating LOP vs. ROP, etc.
I think where you may see more problems or accidents are things like people attempting to make a visual approach instead of an instrument approach in marginal conditions because the instrument approach would add 5-10 minutes of flight time. I've seen people try to declare visual approaches in situations like the video because they didn't want to take the extra couple minutes for an instrument approach. They're looking at the $10 they might save.