That is something that has puzzled me also, never heard a satisfactory answer either.
The answer as given to me back in the 1980s was that a three-step brake in addition to allowing OMO enabled a considerable saving to be made on brake pads.
Previously every Driver drove as they felt appropriate and the braking techniques ranged from light and gentle to hard and rapid. You could sometimes tell the Driver by the way the train handled.
Of course late and hard braking meant that brake pads wore out much quicker, and the brake discs were prone to cracking from being overheated.
Of course much of this also had to do with the need to introduce a coupling system that removed the need for a shunter, as well as the fact that sliding door stock brought with it the difficulty of interfacing the door interlocks into the train braking system, which was why some units only lost traction when the door interlock was lost.
So a combination of factors came together at about the same time. Moving from proportional systems to the three-step was quite a step (pardon the pun) as no longer would the Driver judge where to apply the brake, the technique now became one of selecting the appropriate marker point at which a Step 1 or 2 brake application would bring the train to a stop at the required place (signal or station).
The early units also did not have the ability to completely destroy the air. Step 3 was (if I recall correctly) a 60 psi application. Emergency did not destroy any more air it simply guaranteed that a Step 3 brake application was made by means of the train wires being short-circuited through the brake controller.
Of course another benefit that electronic braking brought about was the ability to operate single manned because there was no need for the Guard to prove the air brake by carrying out a brake continuity test unlike a conventional DMU/EMU following an attachment/detachment.
With the then Westcode systems, train wire 13 or 4 depending upon the stock was a continuous circuit running from the brake controller in the leading cab back to the brake controller in the rear cab and thence back to the leading cab. This "proved" train continuity, as well as proving that the brake controller was in the Off position. This replaced the previous vacuum or air brake pipe.
In an emergency the Guard could apply the train brake by moving the brake controller in the rear cab, thus breaking the continuity in the train wire.
LIke the previous braking systems, the communication cord was provided but unlike those previously, because it broke the train wire, it brought about a complete irreversible emergency brake application, why was in itself a big problem as the Driver could no longer control the stopping point of the train.
I believe that in later builds of rolling stock, the train wire or its modern equivalent is now also interlocked with the doors, and of course it no longer brings about an irreversible brake application, as far as I know