why not use the assumed temperature method first instead of derated thrust?
If you are at a reasonable weight and a speed schedule well above Vmcg/Vmca, no reason why you can't use either approach to achieve the end thrust result.
However, at low weights (typically a ferry or short runway), the decision process involves certification considerations. The AFM pilot requirements are based on the installed rated thrust limits. In turn limiting speeds such as Vmcg and Vmca are based on the limit thrust.
If the pilot elects to depart with a reduced thrust schedule, there is nothing to prevent his/her pushing the power levers up to achieve rated thrust during the takeoff .. say, in the event of a failure. Mind you, if one intends to do that it is appropriate to do it CAREFULLY due to the risk of a thrust exceedance and, at low weights, the very real risk of getting into control problems.
Now, if one uses a DERATED (ie lower certificated) thrust setting, that is the same, conceptually, as unbolting the big engine and replacing it with the smaller one. The pilot cannot command higher than the DERATED thrust setting during the takeoff. The lower Vmcg/Vmca speeds will still apply.
In the real world, of course, we don't change the engines physically but call up a defacto smaller engine either by a fuel control setting preflight (which is not very convenient) or electronic cockpit selection. It is essential, in this case, that the pilot doesn't permit thrust levels to exceed the derate limits otherwise the derate Vmcg/Vmca speeds could catch the pilot out rather badly.
As a for instance, I was involved in the (fatal) accident investigation, quite some years ago, of a twin turboprop which suffered an uncommanded feathering but without an accompanying engine failure.
The crew, apparently, was quite confused by the whole thing and, during the latter stages of the takeoff, increased thrust settings in an attempt to improve the then existing abysmal performance.
End result (with very good spec engines) was that the realworld Vmca went through the roof (VERY rapidly) and it was yaw, roll, and all over, red rover. Fortunately only folks on board were killed but it would have been very much worse had it not been for the existence of the large ditch which took the aircraft out of contention.
While derate/flex wasn't involved, the same over thrust consideration killed them just as dead.