[@ClocktowerEchos]
As you said, Inquisitorial work includes much more non-combat stuff than someone inexperienced in the matter can reasonably expect from any organisation within the 40k universe.

Such non-combat activities, I presume, include both stealthy investigations of different sorts, up to and including undercover work within heretical cults and organisations, peaceful negotiations with other institutions of Imperium, xenos and independent parties, scientific research, recruitment work, acquirement of funds and resources in a manner that does not alert anyone to presence and activities of Inquisition and many other.

As a consequence of his education and creation, a Factor is comfortable and capable of not only parleying between the Mechanicus and Imperium, but also of any other sort of social interaction in any role, all while still keeping his heart hardened, his head cool and his loyalties unswayed. Inquisition needs such people on regular basis and in large numbers in the same way they require a constant stream of warriors capable of fighting the manifold enemies of mankind.

 In the same vein as Death Cults and Crusader orders often have long-term agreements with Inquisitors to supply them with a constant stream of relatively competent yet still expendable murderers, it would, in my mind's eye, make sense for some Inquisitors to forge a similar pact with Mechanicus in order to provide themselves with trustworthy, capable and unremarkable workers that require minimal background and loyalty checks before being put to work - essentially, acolytes coming in in boxes marked as "typical social specialist, one unit".

I'd like to be a factor because it supplies me with an unremarkable background that still justifies my presence in Inquisiton, so that I can distinguish myself pretty much only through in-character actions and feats instead of working off of something that is already there. My idea is to start off as a personality-less living doll that works by uploading behavioural subroutines into his mind in order to assume a needed role, be it that of a grizzled veteran, a charismatic rogue trader or an envoy of Ecclesiarchy, approaching every conversation as a logical problem to be solved through mix-and-matching countless rote-memorized queries and facial expressions until the desired effect is achieved.

Then, later off, I want to slowly make him develop an actual unique personality of his own as he works side by side with powerful and exceptional people and cannot help but begin losing his strictly logical and mechanical attitude, bit by bit, terrified by the fact but unable and unwilling to stop it.