The issue is not not being able to write binary-search; but, given a set of constraints, a very well defined set of steps, and ample enough time; is the candidate able to write it in code what's there in their head (a pretty straight forward algorithm).

I expect candidates to write in code what they can explain verbally, given that the code is do-able in the confines of an interview.

That said, I also get what you're trying to say: Capably implementing Binary Search may not be the best indicator of skill, since Software Engineering is so much more than just converting thought to code.