This is the fundamental problem with "evidence led policy". As soon as science can reliably affect policy outcomes, people who want to change policy outcomes will corrupt the science.
In as much as science deals with things that cannot be affected by policy (ex: stellar physics or nuclear fusion), the "law" doesn't apply I think, except maybe in perception (people may believe that a particular nuclear fusion technique doesn't work even though it's been demonstrated but policy forbade it to be implemented).
For some cases, we would want Goodhart's law to apply - ex: climate change. We'd want actions to be taken to reduce the impact on the planet as we gather and report climate parameters accurately. Similarly, we'd want accurate reporting of gender discrimination in society to result in the reduction of such discrimination. The question really is the way the change is effected. If "salary difference" is an indicator of gender discrimination for example, law makers can pass laws that fix it, thereby removing its effectiveness as an indicator .. but we're happy for even that at some level. That would be similar to a government sending teams to re-freeze melting glaciers because climate scientists are using it as an indicator of global warming.
True policy thinkers, though, would want to ask the "five whys" and work to fix the underlying problem.
Eventually the governments who support technology will win - either via war or economic advantage.
It matters kind of a lot whether the winner is a liberal democracy with free speech and civil liberties or a totalitarian communist dictatorship.
> It matters kind of a lot whether the winner is a liberal democracy with free speech and civil liberties or a totalitarian communist dictatorship.
This is irrelevant to the conversation, but yes that is why we spend trillions on defense technology, so that if it comes to blows we don't lose out.