The word Mayday is not required to declare an emergency. Pan pan still indicates an emergency. And neither phraseology is required as long as the intent is clear, see https://www.faa.gov/air_traffic/publications/atpubs/atc_html...
In fact, it doesn’t even need to be the pilots who declare an emergency https://hsi.arc.nasa.gov/flightcognition/Publications/non_EA...
> The word Mayday is not required to declare an emergency.
That may be so in the US.
But it is a bad habit to pick up.
Especially if you are an airline pilot and you frequently fly to destinations where English is not the first language.
Or indeed in US airspace where you frequently get international carriers flying in and out.
There is a reason why there is internationally agreed standard phraseology for radio communications.
Everyone learns MAYDAY/PAN and the associated expectations around it (e.g. radio silence etc. etc.)
Not everybody will be able to adequately follow along if you have a long drawn-out waffle discussion over the radio ... "we have a little problem" ... "do you want to declare?" ... "oh wait, standby ...." ...."oh, we're ok for now" ... "oh actually maybe this or that"... yada yada yada.
If its truly an emergency then cut the crap and use the standard phraseology and keep the communications terse.