I believe this is the Matrix's version of "It is now safe to remove your device from the computer."
We know that the Matrix is a program that is closely intertwined with your mind and brain in some manner, hence the injuries and death-by-unplugging. It seems that it needs to safely release the resources before a program can be unloaded (The residual self image is itself a program that runs inside the Matrix, but controlled by its owner)
As for the location of the exits: The Matrix appears to be a software system where everything has a physical manifestation within it. There are no non-corporeal program running within it as far as I know. Agents are not system wide search programs, but humaniform programs. The tracer is a pill. A bug is an insect-like device burrowing in your abdomen etc.
So when they load any program into the Matrix, such as a exit subroutine, I think they have to load it to a physical location with a physical form. Hence the telephone booth.