The reality is that generating good questions for a structured interview is difficult. You can't just pose a programming problem. As you've noted, most programming problems have multiple good answers. Differentiating between multiple good answers from different candidates re-introduces subjectivity. Your brain would rather convince you that one valid answer is less good than another, even when it's not, that to admit to you that it can't differentiate or generate a narrative for you. The part of your brain that generates narratives is incredibly powerful and does not care about how accurate your hiring process ends up being.

What we tried to do was create questions that generated lists of facts. "Spot all the errors in this code" would be an example of this approach (but none of the three we used). We went into the process wanting to embrace epistemological uncertainty, generating a historical trail of data that we could retrofit to candidate performance.

In the end, work sample testing was so much more powerful a predictor for ourselves that we never fully got around to analyzing the data. Sometimes we'd get candidates that clearly generated inferior "lists of facts"; I think there may have been 1-2 instances where that outcome actually overruled work-sample testing delivered prior (out of a few tens of engineering hires and probably ~100 interviews).