I blame the legal teams at large companies who are worried that a well-meaning hiring manager will give feedback that could be used in a lawsuit.

Love that your approach focuses on understanding thought process! IMO many companies focus too much on raw technical skills, when softer skills like attitude may be more predictive of on-the-job performance. My team is working to elicit the same signal in a take-home format (since it's more scalable), but I think the best is a combination of the two: short (~1 hr) take-home + follow-up live session on the work that was already started.