Well, I cannot fully agree with all of this.
For example, Bleaches and Blixes use either NTA (Nitrilo triacetic acid) or EDTA (Ethylene Diamine Tetra Acetic Acid) with Iron III salts to oxidize Silver. Some Bleaches, Blixes and Fixes use Sodium Hypo while others use Ammonium Hypo. Mixing these will give a messy set of complexes which may not remove Silver metal fully and may leave a dark brown stain.
As for stabilzers, some contain Formalin and some do not. Mixing the two dilute the active ingredients.
For 2 or 3 part developers, even if they contain the same ingredients the amounts may differ, the pH may differ and the distribution of ingredients between the 2 or 3 bottles of the kit may differ and so you may get zero of a critical ingredient or 2x the amount of one depending on distribution.
That is my reasoning on this.
PE