Let me give it a shot!
For a 4-eng airplane, it is almost always field length limited at lower density altitude. Since there isn't any excess runway avail in a field length limited scenario, therefore, an improved climb is out of the question.
As density altitude increases, 2nd segment climb perf deteriorates. Takeoff weights need to be reduced to meet the climb gradient resulting in 'excess' runway length?!
As such, an improved climb becomes avail. Perhaps, your technical dept has determined, any significant 'benefits' from improved climb is above 4,000'??
As always, I stand to be corrected.
SR