Sorry sonicbum, I do not agree with this reasoning.
Anyway, regarding the multiple runways, what you say is not always correct. Just recently I and all other inbound traffic have been put in the hold on arrival to a major European airport because they had inbound MAYDAY traffic. None of the six runways were available to us, ALL arrivals were suspended until the MAYDAY aircraft had landed safely. And probably for the same reason you mention for a single runway airport: ‘what if someone else messes up’.
Things are not always that black and white.
This is just one example, I can name a few others, but the main point is, calling a mayday will have an effect on everyone else around you, and rightly so. Just don’t forget that if the situation allows, you can always downgrade to a PAN, or at least accurately inform everyone around you of your real level of urgency so that they can assess their own priorities more accurately.