I have declared a Mayday on an engine failure, sump plug fell out was 6 hours after service. Was at 750 ft at the time, 5 miles out, was on the ground 60 seconds and 1.5 mile later.
Paper work was tied up with why the engine stopped rather than calling a Mayday.
The only thing I have noticed with calling a Mayday is, every one goes quiet, I think from experience the controling ATC should run through crash procedures and checks as standard. Your brain is runing flat out and some reminders help.
The main one was keep the air speed up, this kill a friend a couple of years later. Lost te engine on climb out tried a 180 and stalled it in from 100 feet, gentle reminders would have save he's life.