Correctness is important to everyone. Presumably everyone involved would rather software work rather than not work. Time commitments are what they are and sometimes quick and dirty is what you have to do but I don't actually think there is some hard tradeoff between fast and correct. The whole idea of having rigorous foundations is that you have a set of primitives which can compose together in well-understood ways so you can build correct programs quickly without necessarily re-inventing the wheel each time.