Safety Margin
In 1953 the ICAO Standing Committee on Performance, composed of experts from a number of nations published what became known as the SCP-53 report. This report set out to establish safety margins for expected new aircraft, principly jets. It established a method of calculating the variation of parameters for particular operations. As I recall the critical condition for the takeoff case was engine failure and there were about 13 parameters, including the variability of pilot control, density altitude, airfoil roughness, etc. Then for a certain desired incident probability, say 1 in 10 million, a certain margin could be determined. Thus for a twin engine aircraft with an engine failure, there should be a 2.4% gross climb gradient to allow for the variables which might occur and clear a 1% net gradient. A 4 engine aircraft required a 3.0% gradient because it had twice the probability of an engine failure--there were no 3 engine aircraft expected at the time.
For the accelerate stop case, margins where applied to demonstrated stopping distance which I think were 10% for 2 engine aircraft and 15% for 4 engine aircraft. This was not done and the present evolved and very marginal system is what we have; but this is well beyond the scope of your question.
So, for a reduced thrust takeoff, if the thrust is set to have the above stated margins, then theoretically, if an engine fails you have the risk of penetrating a 1% slope of 1 in 10 million; not certain that is the level that was chosen, but you get the idea.
There is an issue of the DC-9 having been allowed to have density altitude correction to 400 feet which erodes the gross gradient margin a little. This was discovered by Boeing which asked for similar treatment on the B-727. I suppose all subsequent aircraft got the same deal. This was called by some: "Southern California Thrust".