This is way better than what we had, so I'm content. I do wish it could have gone further.
Seeking some clarification. If I'm reading properly, Inquisitorial Detachments will still mess with Sacred Rights [Sisters] and Doctrines- anything that requires an army to be mono. Not only that, Inquisitorial Detachments may not even be immune to Battle Brothers, as the rule that provides that immunity comes in the text block that describes how Inquisitors function when they occupy other Imperial Detachments. And finally, as mentioned above, the one Inquisitor per Inquisition Detachment rule means that we can only field Inquisition Vanguards. While we could field a lot of Vanguards, a] some people still believe that the ridiculous limit of three detachments is a rule and not merely a recommendation and b] even if we found an opponent that was okay with it, we could never keep up in the CP race against a faction that has access to brigades and battalions.
As for using an Inquisitor as a part of another Imperial Detachment, the wording leaves some ambiguity about whether you can attach Inquisitors to more than one detachment. I think you can, as long as it's only one Inquisitor per Detachment.
I hope so, because there's a story trigger in my Campaign to bring Karamazov and another to bring Greyfax. I have two other Hereticus Inquisitors with Inferno Pistols as well, and one would likely accompany each of the named heroes. Karamzov would attach to my Penitent Legion, which contains only Priests, Arcoflagellants, Penitent Engines and Repentia. Greyfax would attach to my Sisters Command Battalion. The other two Inquisitors could work with smaller detachments.
But I'd like to see them fix the integration a little bit more, particularly with Chambers Militant.
I think every Ordo should have the keyword of its Chamber Militant, and every Chamber Militant should have its Ordo's Keyword. If it's too OP, I'd be willing to pay CP up front. Alternately, GW could just craft a Chamber Militant rule. Inquisition detachments should be able to join armies of their Orders militant AND Inquisitors should be able to join allied detachments.