I think the idea of taking controllers for jolly's to have a look is a very good one, I've had the chance to watch a radar controller at work. I must admit it totally baffeled me how they manage to make head nor tail of all those blips, respect.
I think the the argument that most of the hassle lies with the airport authorities is a valid one aswell( see below), but I think maybe the controllers need a little more coaching about helicopter operations and capabilitys, especially at airports with fewer helicopter movements.
My experience is, as was said earlier, once they get to know helicopters there's much less of a problem.
I had to fly into Frankfurt (EDDF) one day because there were "absolutley no available parking slots" at the GAT for my company Falcon 50, when I got there the place was deserted, the boss looked at me as though I was total idiot. I was carpeted for being totally incompetant for not getting a slot with no amount of explanation accepted!
An ex RAF controller friend of mine confirmed my plight saying that when EDDF radar complained of traffic saturation, he (stationed in Berlin) used to switch onto their radar only to see there was almost nothing going on ( they didn't know he could do that).
Maybe they should do a shift at Heathrow!