I personally declared two Maydays last year; one was tech related, and the other was due to a sick pax. ... if for example another Mayday call was made on the frequency with a rather more serious problem, for example smoke in the cockpit, putting all souls on board at risk, ATC will prioritise just as they are trained to.
Do you really expect ATC to assess the priority of emergencies rather than those in the cockpit?
Let me flip the situation around:
The left engine on my light twin has a habit of running hot. The right engine does not. On this particular trip, the problem with the left engine appears to have got worse, and, as I'm risk averse, I shut down the left engine as a precaution against a more serious failure. I'm holding quite happily OEO at 5000 ft overhead my destination airport, and have declared an emergency. Now you come along with your sick passenger. Who should land first? Would ATC see it that way if I had broadcast a Mayday?