Sorry, I didn't express myself very well about 'moving to another frequency.' I don't advocate it, but it remains an option in some circumstances (perhaps when you just about to go off the frequency in use anyway) and would not execute a silent change, that would damage the controllers situational awareness. However, I would never say never.
I can see why it is not always necessary to say 'mayday,' but, I still can't see any disadvantages in saying it, it's use does resolve any doubt, it is unambiguous.