Not if they don’t know which gate it’s going to be.
It really is like a train station. Boston’s South Station has one large waiting area, with a food court, bar, newsstand, and chairs and tables (but not enough during rush hour). And there’s a big display board (visible to pretty much the whole room) that says which trains are boarding, on which platform, and when. When the station is crowded, you can’t tell who’s waiting for which train, but when a train and track number is called some portion of the throng makes it way through the doors and out to the platform.
The only big difference at an airport is that the gates are farther apart. It seems like as long as they called it far enough in advance for everyone to make the walk, there’d be no problem. If you’ve got a suitcase you want to stuff in the overhead bin, just watch the board like a hawk and set off at a brisk walk as soon as the gate number is called.
If anything, I would think airlines prefer the usual arrangement, with each gate having its own waiting area. Every moment an airplane sits on the ground is time that it’s not earning any money. They don’t want to wait for any stragglers who might have been in the bar and didn’t hear their gate number called. They want everybody where they can keep an eye on them; make flight-specific announcements, figure out if anyone from the waiting list gets on, etc. Then when the plane shows up, they want it turned around as fast as possible. (“Bodies off, bodies, on, and boogie”, as I’ve heard it said.)
Talking about trains in Europe (and I assume it is similar for air traffic), the tracks are assigned half a year up front… but there can be as many as 10 departures an hour on each track, maybe more. Any small delay could mean the tracks have to change or that a bunch of trains need to be reassigned to different tracks. This makes waiting with the communication kind of logical. In Germany they do announce changes from the “normal tracks” btw.
That’s standard. But load / unload time is much faster for trains (more parallel than planes) and there is usually little or no servicing involved.
Besides the fact that US airports would have to be significantly reconfigured for this, you have other problems. Those in wheelchairs would need to get moved right away, and if there were a few flights taking off close together (common during rush times) you might have a shortage of people who can push them.
As you mentioned, people can get lost. Announcements don’t happen all over the airport, and they don’t often get heard. Today a person who isn’t on the flight but whose luggage is causes a longer delay than before. You’d have to build the central waiting area for peak traffic - the size individual gates depends on the plane, not the hour, unless there are delays and two planes worth of people show up.
Finally with upgrades there is a lot of interaction between the gate staff and at least some passengers. This is going to be harder to manager with a central service desk. Then there is the problem of whether the seating area is owned by the airport or the airlines.
Early airports—well into the jet age—were planned like train stations. One big common waiting area with services, and when the flight is announced for boarding, people go out the concourse to a specific gate. But for some reason travelers behaved differently than they had in train stations, preferring to go immediately to the small lounge areas near the gates. By the time O’Hare opened around 1962, designers had arrived at the scheme we’re familiar with today, with the obvious exception of Dulles, only recently retrofitted.