Here in the USA all airport website that I have visited always show the gate number. Available many hours before the flight. Even better, the airlines websites show it too. My boarding pass, either printed, Apple Wallet or the airline app, shows it. Heck, I just enter the airline code and flight number into Google and it spits out everything, including gate #.
I looked at Manchester, London City and Gatwick websites. Manchester seems to show gates for all flights, the other two, only for soon to be boarded flights. So you do have a valid point.
Pardon my ignorance, but in the USA we all congregate & wait right at the actual gate where the jet ramp is, all open to coming and going. My limited travel to the UK has me remembering that there is some sort of common area for many flights and only when it is near flight time is the actual gate area w/boarding jetway, that is near the common area is announced & used? Is that what you refer to as a "gateroom"?
That said, I rarely use any airport website for arrivals / departure info with so many other ways to find it. Mostly I use it to check all flights when I schedule my own plane flying so I don't have to wait 20 minutes idling at the hold short line waiting for landings and departure airliners.