On top of these skills, you actually need most of all software engineering and architecture experience. I don't think this is common in academia at all. Not in professors, not in PhD-students. You need practical experience building complex software at a large scale. Across that, you need to implement these CS fundamentals.

This is requires far more CS than you'll find in your usual software development effort, for sure, and many CS professors absolutely fit that bill. However, to the same degree it also demands far more on the software engineering side. People out of academia in general, from every time I've seen them build software, have not been all too impressive on that side of things.

Web search has an incredible demand for being well rounded, beyond anything else I've encountered. CS isn't the hard part bottle-necking everything else, it's just one of the many hard parts.