You're the CEO of a utility corporation that proposes to build a nuclear power plant, of innovative design. After a detailed and objective study by a team of actuaries, engineers, and lawyers, your CFO tells you that one particular feature, described by the designers as a safety requirement, is not cost-effective. No government regulations compel you either to implement the feature or to leave it out. It's your decision. Do you implement the feature?
Answer: Yes, of course. If you don't, the power plant won't be safe; that's what ‘safety requirement’ means.
The argument on the other side is that the feature will do more harm than good -- the potential benefits are less than the implementation costs. That's what it means to say that the requirement is ‘not cost-effective’.
But this is not quite true: A course of action is ‘cost-effective’ when the potential benefits to the corporation are greater than the costs to the corporation. It generally means that the costs can be externalized -- someone else will pay them, while the corporation receives the benefits. It does not mean that those costs do not exist.
In the United States, the costs of operating unsafe nuclear-power plants are externalized by the Price-Anderson Act of 1957, which limits the liability of plant operators and makes the government of the United States the “insurer of last resort” for nuclear disasters.
Addendum. A recent post at On the commons explains why mainstream economists ignore negative externalities.