It sounds real simple to say "plan where every train is going to go ahead of time." And believe it or not, they actually do that. All the switching at Penn is computer controlled and programed in advance. The problem is that reality intrudes in the form of a brake problem, or a medical emergency, or a late train. And then the plan goes right into the dumper and track assignments get changed.
I was talking about NJT and LIRR commuter trains, not Amtrak at Penn. How often do brake problems and medical emergencies happen on commuter trains?
Also, I know switching and dispatch and platform assignment is all done computerized and pre-programmed, in fact that's the reason I feel it a bit amusing that they don't tell the passengers fairly in advance which platform they should expect the train. You should someday visit, or see some videos of Churchgate train station in Mumbai, India. There are close to 800 commuter train services operating out of the station per day, and like NYP it is a stub end for the commuter trains, so each train pulls in from the south, waits for a few minutes and starts its journey back north. At the station concourse there are television screens that display the next two scheduled services expected at each platform, you look at it, find a suitable train for your destination and walk to that platform and wait. No crowding in the concourse. Yes, sometimes a train gets delayed and cannot vacate the platform in time, in that case the next scheduled train into that platform waits outside the station for a couple of minutes and then pulls in. There are rarely last minute platform substitutions. Most trains have five to ten minutes turnaround time, so if it arrives two or three minutes late, the delay is absorbed by the turnaround time and it can still start its return journey on time. It is better to let a train move in two minutes late rather than re-assigning it a platform at the drop of a hat and making thousand passengers run amok every few minutes. If this system works well on a daily basis in an Indian system which is quite technologically backward compared to some European and Asian countries, something similar can surely work on our rail systems here which have fair amount of technology incorporated into it.
First, let me say that it's always hard to compare operations because there are so many variables with things.
That said, please correct me if I'm wrong, but Churchgate really is a stub end terminal. NYP is not. There are actually very few trains out of the greater hole that change ends at NYP. Then there is the fact that the LIRR is coming in from the east, while NJT is coming in from the west. And again, both run the majority of their trains through the station, the LIRR to the West End Yard, NJT to Sunnyside yard or loop. Then toss in Amtrak which arrives, often late, from both the east & west.
Now I did a quick search, but could not find out how many tracks Churchgate has to handle those 800 trains. Penn on the other hand has 21 tracks with only 6 throat tracks (a very limiting problem) and according to the Gateway studies, 1,248 train movements each weekday.
Next, at NYP during rush hour most trains have at most 10 minutes on the platform, save Amtrak's trains. In fact, it is not uncomom for a LIRR track number or NJT track number to pop up on the board and the train isn't on the platform when you get downstairs. It pulls in a minute or two later, loads up, and is gone.
Next, while I'm not a frequent commuter rider on either NJT or the LIRR, just based upon my observations which are not extensive at all, I'd say that at least 3 or 4 times a day a train ends up on a different platform at the last minute. I know this because many regular commuters have indeed learned the "schedule" and therefore which platform there normal train home will be on. So when there is a track change, the announcer harps on that point repeating multiple times "this is a track change" in the vain hope that those who went down early will pay attention and come back up to change to the correct platform.
Many do, but invariably there are those with their music on who never hear that announcement and either board the wrong train or if they're lucky realize that something did go wrong and come back up to catch the next train to where they need to go.
And of course some days things go horribly wrong with a train lying down in one of the tunnels where almost every train ends up on a different platform than is normal.
Finally, there is the issue that in most cases, the platforms simply aren't wide enough for people to be standing around waiting for their train. This is quite probably the biggest reason that Penn doesn't put up track numbers until 10 minutes before. You could have two commuter trains pull in, dump their loads, and then pull out to the yard. If half the load for the first outbound train is already standing the platform, then you cannot get the people off those inbounds and the inbound trains out of the station in time to bring in their outbound train.