I fell into this rabbit hole for the first time about five decades ago, when I stayed up way too late and caught A Night To Remember on broadcast TV. Let's see if I can provide enough of an answer to pass muster.

I'll write about MAYDAY, work my way backwards in time for previous distress signals, and then summarize why it became an international standard.

OK, so MAYDAY is a proword (procedure word). It was definitely influenced by the French "m'aydez", but to be clear it was a deliberate construction. Frederick Mockford of Croyden airfield created it specifically as a distress call. Regardless of the origin and inspiration, it means "urgent distress".

The telegraphic distress signal is SOS, and pre-dates the verbal MAYDAY.

The SOS signal is a prosign (procedure sign). It's technically a single sign consisting of the pattern "dot dot dot dash dash dash dot dot dot", with no spacing, but sending the sequence of the letters SOS is close enough for nearly any purpose. The letters "SOS" are not an acronym. People have back-constructed phrases like "Save Our Ship", but in fact the pattern was chosen to be distinctive as a pattern, not to capture a phrase.

SOS is not as old as telegraphy itself though. There was no common "distress signal" for land telegrpahy over wires. With the advent of wireless telegraphy, a need arose. "CQ" was already a land-telegraphy prosign, meaning "All Stations". The Marconi company, the earliest provider of wireless telegraphic equipment, suggested "CQD" as a general distress call.

CQD itself was a new prosign (like SOS) and not an acronym. "Come Quickly, Distress" for example is a good mnemonic but it's not what "CDQ" stand for.

CQD was adopted by most early users including White Star Line. There were not many actual uses of it recorded. One famous use: in 1912 the Titanic's telegraph operator sent both CDQ and SOS.

Before the radiotelegraph there were other distress signals, with varying degrees of recognition. An inverted national flag; three shots of a cannon; a square flag or panel over a round flag or ball. Many "flag codes" included a distress signal, or even several giving more information about the nature of the problem, but these could be specific to a certain navy or shipping line. There was no true international standard. In modern usage the flags representing "NC" can be used to indicate distress.

So, why did MAYDAY (and SOS) become widely used?

Adoption of both MAYDAY and SOS occured via the International Radiotelegraphic Convention. SOS was adopted in 1906, and MAYDAY in 1927. As to why specifically MAYDAY succeeded at this convention, I can't say. I'd love to see some minutes of the debates. But becoming a standard was the crucial step to international usage. These standards were taken pretty seriously, and standards often referenced each other. For example, the International Convention For The Safety Of Life At Sea (1929) in the chapter to radiotelgraphy requirements for shipping, referenced the International Radiotelegraphic Convention of 1927.

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Article 32

Competence

The matters governed by the International Radiotelegraph Convention, Washington, 1927, and the Regulations annexed thereto remain, and will continue,

Edited to fix formatting.