Certainly. I'm not sure it's as infrequent as you might think.
OK, so lets assume it is more frequent than I had imagined .. .. ..
so there are two aircraft on frequency both "working" a mayday.
So whats the chances of them both arriving at the runway at the same time, even if ATC dont prioritise?
I appreciate ATC do not want a blocked runway and that may be a factor in prioritising, but I would far rather they do their job in terms of assessing who is most at risk, and who should go where, and leave me to manage the aircraft - after all I am not sure I want anything else to worry about.
In short maybe your argument actually supports declaring a mayday.