But what is the relevant "duck" here? What actual dynamic is the law trying to enforce? Any good law tries to align individual incentives with a social optimum, and I don't see how it's doing that here.

As best I can tell, employment law is trying to achieve the goal of "to the extent that you make a person economically dependent on you in the short term, you must provide that person some benefits that make up for that dependence". Hence why contractors get treated one way and employees another.

But then the law goes about it the wrong way by having a sharp discontinuity that encourages employers to make the relationship such that they get all of the advantages of such dependence, but stay just on the side of "you're still a contractor". For example, as it stands now, employers strengthen their case by making the worker bring their own tools.

A sane law would be more continuous: as you introduce more dependence of the worker on you, you most provide increasingly more benefits to cancel the problem that introduces. Though I admit that would involve a huge refactoring.

Trying to resolve whether someone "is" a contractor is (in the grander scheme) asking the wrong question, like debating whether alcoholism "is" a disease (cf Scott Alexander's "non central fallacy" or "worst argument in the world").