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The purpose of the equalization pulses was to eliminate any horizontal rate energy around the vertical sync pulse. The idea was that if horizontal pulses got into the vertical sync, they would cause line pairing (loss of interlace), so twice-horizontal rate equalizing pulses were inserted. If these get into the vertical sync, they will help trigger vertical on an exact half-line for good interlace.
Since the vertical sync separator circuits always use ordinary ("minimum-phase") circuits that do not look into the future, the post-equalizing pulses are essentially useless. A truly good vertical sync separator circuit doesn't need any equalizing pulses, so this was a lot of complication for not much benefit. Later digital sync separators did a pattern recognition of the vertical sync, and locked it to twice horizontal, so effects of analog integration were no longer relevant. These circuits, introduced shortly before VCRs came into use, eliminated customer hold controls, and could synchronize on signals so weak that the picture was unrecognizable. These super stable circuits had to be modified to follow the erratic sync timing of VCR playback and non-standard sync of video games, resulting in some degradation on weak off-air signals
The equalizing pulses also have a detrimental effect on horizontal sync. The original idea of the NTSC sync waveform was that the receiver would sync horizontal on the falling edge of H sync, but trying to use the full-bandwidth sync edge gives very poor results on weak, noisy signals. So, all receivers filter the sync waveform to remove noise, resulting in H sync being more towards the center of the sync pulse. If you look at the equalizer pulses, they are timed so that the falling edge matches H sync pulses - but the centers do not. This, combined with similar timing issues of the vertical serrations, means that a receiver that is good for weak signal performance will also pull the horizontal sync phase a bit during vertical blanking.
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