A lot of folks getting too involved in the weeds level, here ... considerations are all to do with certification ..
(a) takeoff performance starts with the AFM stall speed for the weight.
(b) AFM stall speed usually is determined at the forward limit for reasons tied up with the tail download consideration mentioned in several posts above .. ie the forward limit normally gives the highest flight test stall speed within the envelope CG range at a given weight.
(c) the consideration is a bit like derate in that the OEM is perfectly entitled to do several mini-certifications for the aircraft. In the same way derate lets the operator take advantage of lower Vmcg/Vmca, restricting the AFM forward cg limit permits the operator to take advantage of a lower stall speed for a given weight . .this lower stall speed then flows into the other speeds pertinent to takeoff speed schedule and comes up with a few extra kilos RTOW especially for runway limited circumstances .. this may not apply at lower weights if the basic performance is minV1-limited.
(d) in all cases, to take advantage of the permission, the operator has to have the supplement in the AFM (generally at humungous cost .. it has always ever been .. and will always ever be ... the same)
(e) In simple it is a method of degrading the safety margin in order to operate the aircraft from limiting airports safely.
Not quite .. the minimum "safety margins" remain the same for certification .. what the OEM is doing is a multiple certification .. a bit like having two slightly different aircraft models within the same Type
(f) technically speaking, you should have the tool to calculate takeoff-data for each CG position within the env
Those of us with the tech background could come up with some plausible data .. however, at the end of the day, the operator can only operate within the boundaries of the AFM .. so, if secondary CG limits are not published then this argument remains academic.