> I admit the style of interviewing I'm describing has its own problems

We need to be clear, ALL styles of interviewing has problems. There's no global optima for problems like this. It's important to say this because people will point out problems as reasons not to switch while ignoring the existing ones. The answer entirely depends on "what are you optimizing for?" Be precise

Also worth pointing out, the style you describe is the traditional engineering interview. Leetcode type problems were initially done this way. It is also easy to make an effective system worse by trying to improve it. This often happens by trying to apply hard metrics to noisy problems. You don't improve your accuracy, you are just fitting a certain type of noise better (and encouraging Goodhart's Law).