Resistance to the positive side of the power supplies is not an issue with regular traces, so logically the same would be true of the ground side as well. Why use an entire plane for the ground supply when that layer could be used for all sorts of other routing as well?
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There's some truth to the screening effect but it is all too easily overstated. In practice a ground plane often has limited usefulness as a screen, since so many signals pass straight through it, and it does absolutely nothing for other sources of interference.
The real principal reason is the speed at which a lot of modern electronics operates. At high speed, signals take a non-negligible amount of time to propagate from one end of the trace to the other, and then reflect off the ends several times. These echoes quickly die down, but during that time the device at the other end may already have read an incorrect value. How fast the signals must be depends on how long the traces are - for the speed of machines like the first PCs the traces could be tens of feet long, making this issue almost irrelevant, but at modern computer speeds it becomes critical on traces longer than perhaps three or four inches.
To prevent these echoes the traces need to be considered as transmission lines, and correctly terminated with resistors to absorb the signals so that reflections do not happen. However, the value of the resistance to use must match a property of the trace itself known as its characteristic impedance. For a single wire this is impossible to predict, since it depends on what is around the circuit and even the logic levels of neighbouring components. You can't terminate a trace with those unknowns. The ground plane ensures that the relationship between the trace and ground is the dominant one (due to capacitive effects between the two, on separate but parallel layers). The characteristic impendance is then well known, and indeed can be varied by altering the width of the traces. This more controlled environment then means that the correct value resistance can be placed on the end of the line to cancel out the echoes, before they cause a malfunction.
The real principal reason is the speed at which a lot of modern electronics operates. At high speed, signals take a non-negligible amount of time to propagate from one end of the trace to the other, and then reflect off the ends several times. These echoes quickly die down, but during that time the device at the other end may already have read an incorrect value. How fast the signals must be depends on how long the traces are - for the speed of machines like the first PCs the traces could be tens of feet long, making this issue almost irrelevant, but at modern computer speeds it becomes critical on traces longer than perhaps three or four inches.
To prevent these echoes the traces need to be considered as transmission lines, and correctly terminated with resistors to absorb the signals so that reflections do not happen. However, the value of the resistance to use must match a property of the trace itself known as its characteristic impedance. For a single wire this is impossible to predict, since it depends on what is around the circuit and even the logic levels of neighbouring components. You can't terminate a trace with those unknowns. The ground plane ensures that the relationship between the trace and ground is the dominant one (due to capacitive effects between the two, on separate but parallel layers). The characteristic impendance is then well known, and indeed can be varied by altering the width of the traces. This more controlled environment then means that the correct value resistance can be placed on the end of the line to cancel out the echoes, before they cause a malfunction.