choose how the orders go, not just that they go

Downmix takes a high-order field and produces a lower-order one. The point is that you get a choice about how, and the choice is audible.

This is the most common thing that happens to a mix on its way out the door: a delivery format accepts 1st order, a game engine runs at 3rd. Something has to decide what becomes of the detail that no longer fits, and discarding channels is only one answer among several.
The modes trade the same things in different proportions — how tight the image stays, how even the field is as you turn, and how much of a reverb tail living in the higher orders survives. There is no correct one. There is one that suits the material.
Folds discarded energy back into the lower orders, so what you built is still audible.
Re-records the higher-order field through a virtual array, trading precision for the character of a real one.
Offline. Analyses the field at over 200 points and re-encodes what it finds.
The cheapest and sometimes the right answer, with optional max-rE weighting.