I don't know of any AAmb which would launch just to keep the stats up
Oh, there's at least one!
Last year (or was it the year before) they flew over 50nm to attend a teenager with a broken arm at a weekend rugby match, when there was a Minor Injuries unit just over half a mile away by road! The Ambulance Service didn't ask for them, but it would seem that they heard of the incident and decided that there might be a good opportunity to show themselves off in front of lots of potential donors. Rather pointless, especially when you consider that the hospital the yoof was taken to was 45 mins drive away (handy for the parents!), when he could have been treated in his home town...
This isn't an isolated episode either. One definite benefit of central funding of Air Ambs would be that they wouldn't then feel any pressure to justify their existence by launching to every incident they hear of, no matter how inappropriate that incident may be for them to attend. Don't even get me started on Air Ambs having a go at mountain jobs and then having eventually to admit that they can't get the casualty and calling for SAR, enormously prolonging the casualty's stay on the crag/hillside...