Why Are There Master Numbers?

My response to your first two questions is that numerology is based on observation and experience. Thus, there are master numbers because it has been observed that when people with double-digit calculated results in the core numbers tend to have different experiences or tend to have different characteristics than those with one-digit numbers that were reduced from non-master numbers.

I have seen master numbers mentioned in numerology texts written in the early 1900s. But I have never read about who or which methodology first tested master numbers.

Your third question contains an incorrect premise. Master numbers can be reduced down and there are situations where it is prudent that it be done. See Master Numbers and Potential for more information about that.