The engine guys are likely to propose this:
The transient (taxi idle to TO) is a major parts-life consumer. Using the highest FLEX temp (lowest EGT) minimizes this transient, and that's a good thing for engine life.
Once the engine has been running at TO for a minute or so, it's pretty well warmed up, and thus a push up to CLB is a minor EGT transient; and if that push saves trip fuel, with negligible wear & tear, then that's a good thing.
In other words, breaking the whole EGT picture down, splitting the big transient into two parts is an optimized operating cycle from a hardware standpoint.
(Even though the average pilot finds this counterintuitive...)