I very much agree. In January I went to Glasgow Airport to pick up people from a flight which was shown on time, both on line before leaving home and on the screens within the terminal; Until it disappeared from the screens! What had happened to it - Had it landed, crashed, or diverted via the Bermuda Triangle and been abducted by aliens? There was no information, no announcements and no staff to ask either, until I eventually found someone by wandering to a different part of the airport and asking them. It transpired that the landing at Glasgow had been aborted at the last minute (due to high winds) and diverted to Liverpool. I did complain to Glasgow Airport, but it was a waste of time and electricity.
The problem with airport screens is there simply isn't enough room to display what's happened to the flight. Even "go to desk" is pretty meaningless. Which desk? Where?? Whose? Airside? Landside?? Will there be anyone on it?? To me, a bit like Euston although Euston is nothing like as bad, yet, pax information has been sacrificed for more advertising space. I was once stuck on the Isle Of Man with flights trying to land, and then diverted. Not a sniff of info on the ground.
In the old days before screens, both the rail and airports had those "flip-round" screens, where the majority of eventualities was covered; I remember them well at Piccadilly station! But if there was something not covered there was always someone to ask, and if they didn't know they'd get on the phone and find out!
To be fair r/e rail, the amount of information we can find these days by ourselves is remarkable and I can imagine the day when pax information screens are discontinued (or, like Euston, replaced with ads, grrr...)