It's a Human Factors thing
The argument about the meaning of the words "mayday" or "panpan" or "emergency" I think misses the point.
Human beings, though we like to think we live in realtime, have a perception the lags behind reality by varying degrees. For a completely anticipated event it may be a small fraction of a second, but for the completely unexpected it can easily be over a second - maybe two.
It has been decided by people who know a lot about these things, that a two syllable word, with a clearly understood meaning, repeated distinctly three times, is just about the right amount of time to get everyone fully tuned into the situation and ready for the detail that will inevitably follow.
The potential problem with saying "Emergency" just once is that you could then be several words into the detail by the time a busy controller becomes fully alert to what is after all an unexpected call outside the context of his/her current mental air picture. Momentary confusion, and a failure to understand at least part of the message is likely to result.