the QNH set in the cockpit in TC (Although for some aircraft types, it doesn't always work properly)
I've noticed this too but have never been given a reason for it. Best guess from me is that the certain aircraft types have a 'standard pressure' button when above transition, and then they turn it off for below that, so they never actually change the QNH pressure setting until arrival. Might explain why the downlinked pressure is wrong (and probably dep qnh, I should check this at some point when quiet!)
as for
[Of what practical use would the controller make of IAS anyway ?
Very handy on windy days when two inbounds from different directions are going to get fairly close at a common point, it leads to much more efficient streaming, especially if neither is yet in your sector.