"Wouldn't a double yellow line do the same thing?"

No. "Keep Clear" means "Don't even stop here in slow-moving traffic." Same sort of forward thinking needed as for pedestrian crossings (you shouldn't be stationary on them, even in traffic) or box-junctions (don't enter unless the exit road is clear).

.......... or maybe obstruction

dvd

We have "Keep Clear" markings on the road outside our Police and Ambulance stations but our Fire Station has yellow hatching. Obviously a double yellow would be no good in either case as this would not prevent you obstructing the exits. In the case of the Ambulance and Police stations, you would probably not even be aware of what they were unless you were local.

Don't really see the need for keep clear markings at obvious places like entrances to fire stations, hospitals and the like, it's common sense. I always leave side roads clear when I reach a line in traffic. It's just common courtesy IMHO

The answer from daveyjp seems to fit the bill. So why doesn't the council save some money and use Keep Clear markings instead of yellow lines and save the likes of you and me some money I wonder? Best Regards.

You can use double yellows over a long distance, miles if you want, but "Keep Clear" markings can only be used for a short length of road. Also, double yellows are purely to control parking, they don't keep a junction etc clear. They are totally different animals.