It is certainly important to look at images but it has to be done as the last step IMHO, here is, doctored, what I was writing on Slack last week:
I’m taking the exercise with three principles:
- The outliers we are trying to bring inside the working space, are naturally narrow-band and extremely saturated sources, so I want to preserve that quality at all costs, we should not be taking too many creative decisions at this stage, I don’t think it is the purpose of this group.
- I would like the solution to be defect-free as if we were doing a plane, very smooth curvature, I was playing with qualifiers the other day and curves with a kink can produce defects when grading.
- Has to be elegant, the RGB method is extremely elegant in that sense.
I think the first point can be assessed without any visual tests, if the compression function we pick, reduces colour purity too much, it is not good.
The second point is a bit harder, you take it from a mathematical standpoint and enforce/strive for C2 continuity (as much as possible) which Tanh/Arctan or a custom spline can do but not the others as you get a kink with them.
The last point is easy, less code less operation and simple design primes 
Now for the context(s), there are many and it is entirely viable to use the Gamut Mapping operator in other pipelines than the strict ACES one, especially because it is agnostic. However in the context of ACES where the transformations are immutable and without user control, we, unfortunately, don’t have too much choice.
This resonates with this post I just made here: Notice of Meeting - ACES Gamut Mapping VWG - Meeting #15 - 6/4/2020 - #6 by Thomas_Mansencal.
Let’s assume that we have determined good thresholds for the various cameras and we ship a dozen of LMTs for them. In one year, the IDT Virtual Working Group propose new IDTs that are bringing values in AP1 or extremely close to it. We would have to ship another set of Gamut Mapping LMTs. The subsequent year, the RRT & ODT Virtual Working Group propose changes that make the parameterisation of the Gamut Mapping operator sub-optimal, we then have a dozen of LMTs to update in a backwards-incompatible way.
This also supports the reasoning that while it is critical to perform to visual assessment, it should certainly not be our single prime metric because what looks great today, might simply not tomorrow.
Cheers,
Thomas