Okay, we've discussed our options and have come to a decision.
The site rules for discussion of Inquisition armies are going to be adjusted to bring them in line with the other armies.
Inquisitorial armies as primary detachments may be discussed. However, if the allied detachment is not a codex covered by the B&C, the Inquisition primary detachment must include at least two elites choices.
Basis for the change:
First, it's unfair to exclude the Inquisition as a primary detachment because GW allows such to be done. More importantly, the Inquisition as a primary detachment can be done with a codex that we discuss as the allied detachment (e.g., Imperial Guard). Such armies are perfectly valid here at the B&C as they remain in keeping with the site identity.
Second, the artificial requirement for two elites slots when allied with xenos (Eldar being the only valid case), puts Inquisitorial primary detachments on par with the other codices covered here. This is an increase from the official requirements, but the purpose is to provide some degree of freedom to players while maintaining the site's basic identity. Two alternate options were to either prohibit Eldar allied detachments entirely or allow them to go whole hog, both of which had drawbacks (just as this option does, admittedly). In the end, this requirement is a compromise solution that should work well enough for most, while we know that it will be objectionable to some (on both sides of the issue). This still allows for things like a minimum-sized Inquisition-based primary detachment with a much larger (i.e., more expensive) Eldar-based allied detachment, but this sort of "abuse" can be done with any other army that we discuss here at the B&C so we don't want to create too many exceptional allowances for the Inquisition that would be discriminatory.
Note that the requirement for dataslate formations to at least be from the allied detachment still stands, so you can't take an Inquisitor and two Stormtrooper squads for your primary detachment, a minimum-sized Eldar-based allied detachment, and a bunch of Tau formations.