Why should one? Perhaps they should if it's relevant to their work, daily routine, or interests. But if they have no need for it?

Needs are all fabricated, Ludwig Wittgenstein said "the limits of my language are the limits of my world", the same thing happens with logical thinking and all its tools including math.

Well, I think one should be able to come up with a way of doing so on the fly just from knowing that the square root function is monotonically increasing, and knowing binary search? Of course, doing it another way might be more efficient.