[nemetroid]

I think the question is easier to answer if it's flipped. Why can't other engineering disciples work fast-and-loose?

The answer is that for software engineering, the cost balance between "working fast" and "avoiding errors" largely works out in favour of "working fast", even with the potential error rates factored in. In other engineering disciplines, the cost of failure is higher (often much higher), and therefore "slow and steady, avoiding errors" methodologies win out in this balance.