My military days we had "minimum fuel" to get priority which would upgrade to a "Pan" call meaning urgency and then a "Mayday" meaning emergency...
That is what we should have. A clear concise description of the situation with common sense logical steps.
Adopting "Mayday" and added a word to it diminishes the original intent of the word.
An expected landing with less that the required fixed reserve of fuel should be a "minimum fuel" call.
Just because it has been used overseas for yonks does not make it logical or correct.