Since no one seems to have given the answer to the original question….
I believe the problem with FLEX/ATM method is that by definition it lowers the thrust as much as possible, to make use of the entire runway. So, unless you are limited by climb/2nd segment, ATM method will give you zero (or almost zero) stop margin, regardless of the weight you’re taking off at.
OTOH, FIXED de-rate is by definition fixed - as mentioned by others it’s just like bolting a smaller engine. So with fixed derate, unless you happen to be exactly on rwy-limited RTOW, you will get some stop margin…
And since rwy friction is considered unreliable on contaminated runways, the regulators want you to have some extra stop margin…
Hope it makes sense…