This style of interview works in plenty of other professions that are much more rigorous than software development. You'll be hard pressed to find an aerospace

This style of interview works in plenty of other professions that are much more rigorous than software development. You'll be hard pressed to find an aerospace engineering company that is going to ask candidates to evaluate integrals on the whiteboard that they'd normally look up in the CRC or implement a numerical solution for (probably using a prepackaged library), for example. Yet you're proposing an analog of this very thing here.