Interesting thread, there is a way forward - again, referring to the UK in the main as this is what I know a bit of, and it is were the incident took place.
As ATCOs, we always ask what the nature of the emergency is when a pilot calls a PAN or MAYDAY. As an area controller, I or my supervisor would pass that on to the relevant people, including the tower at the airfield the aircraft was going to.
It is easy enough to categorise PANs for different levels of response or call out, levels of response that would be commensurate with the emergency.
A MAYDAY due fuel, when the pilot states he might not make the runway, would get the whole shooting match out, whereas a PAN due to the A/C landing below the required minima, as per the posts above, would not receive the same reception i.e. fire crews would not come screaming out from all manner of places etc. (The above are just very simplified examples of how one could categorise emergencies).
Emergencies in military towers certainly used to be (and maybe still are) dealt with in this way, whereby an emergency broadcast is made, and amplified by telling any members of the emergency services that are not required to stay put (but in not such a verbose manner!)