I feel there is still a basic misunderstanding here.
Do not confuse “processing profiles” with “input profiles”. RawTherapee’s default processing profile for raw photos, as well as the “neutral” processing profile, both use an input profile - a simple color matrix at the very least, and all the other stuff a full-fledged DCP contains (ColorMatrix, ForwardMatrix, HueSatMap, LookTable, ToneCurve) if one exists.
Also worth bringing up, to throw a monkey wrench in the works and complicate things more, as anyone who’s used tone curves in RawTherapee knows, the same curve shape can lead to drastically different results based on the tone reproduction operator, the “curve mode”. Accurate (in what sense?) vs aesthetically pleasing. So there’s also that to consider.