I think the vast majority of conscientious and professional pilots would prefer a small delay to a hurried re-plan of the departure.
No one is afraid of reverting to raw data when necessary, but it's exactly that type of thing that leads to a reduction of situational awareness in the crew, with all its attendant dangers.
Years ago we did it all the time, nowadays we have a lot less accidents. Perhaps there's a connection there?
Better a few seconds late in this world, than a few years early in the next.