Agaricus,
I stand to be corrected but I believe a lot of the ATC / airport emergency procedures stem from years back when, with less spare power and redundancy, the loss of a hydraulic system or engine was a major issue for a large aircraft. Sadly as aircraft systems and performance have improved, the liability culture seems to have worsened and I suspect few airports would be keen to downgrade their emergency response criteria.
And in no way does it subvert the PAN/MAYDAY system - that's just to get you down safely and as expeditiously as you want. The number of trucks that meet you later is almost a secondary matter, although we appreciate it can be bad
PR from the passenger viewpoint. Often, for a "local standby" the AFS will stay at a discreet distance and follow you to stand rather than surround you with excitement and blue light...