There is a whole world of development that is OS specific, UI specific, shipping commercial applications. Shipping quickly is always a higher priority than performance, because adequate performance is usually trivial to implement with hash tables/arrays/linked lists.
Are you sure about that? What if your code has to work for billion plus people correctly 99.999% time who are on all different kind of connections?
I would also argue that make a very clever algorithm do correct stuff (and be maintained to do that in the future) is more difficult than do it using simpler method/algo.
I you need to write so performance critical code that the choice of tree structures matters then this interview question sure as hell isn't going to find out if you are cut out for it.
In fact, I would argue that one could know how to write one and have no idea of the practical use of it.