One of the main drivers for having the third runway full-length is that it will supposedly allow a symmetrical operation that would provide predictable, equal respite for communities under all three approaches.
If the new runway could only be used principally for arrivals, then distributing the respite equitably would not be possible.
Having said that, even a full-length third runway would mean that communities under the current approaches would have respite one-third of the time, instead of the current 50%.