Groundspeed on the radar: that would be nice! Oh yes, I forgot, that's what we will be getting for £700m when the new centre opens!
Seriously, though, we live in a somewhat archaic world in UK ATC where aircraft FMSs can fly a track (eg 3nm offset) far more accurately than we can steer them using radar headings, but we are still required to use radar headings to provide separation between traffic at or crossing the same level. The reason for asking for IAS and HDG is that then, as my UAE colleague points out, we can be sure that everybody can do that. We can always adjust the heading as necessary. That's why you often get 5 degree adjustments. I think most controllers are capable of recognising that the track and GS will change as altitude changes.
One thing which does astound me, however, is how many people ask an aircraft its IAS at, say, FL350 and then tells it to maintain that in the descent without realising that this is VERY slow once you get lower down. It is for that reason that I use the phrase: "When using IAS, speed no more/less than xxx kts". Then everybody knows where they are. The use of mach numbers for speed control in the climb/descent is source of hours of amusement!