Why can't this happen? Now, this could go off in a number of different directions quickly, and I know psykers aren't liked by most people in the Imperium, and playable ones aren't always so popular here, but the Inquisition is rife with them, several of the most powerful Inquisitors (Coteaz, Eisenhorn, Cain) are undoubtedly psykers of various strength levels, and most don't have the broken, stooped, look of the typical men and women whom the AAT (I just realized how close that is to AT&T, and with the job of astropaths in RT, if it HAD worked, I'd be laughing too hard to type; if you are one of those Verizon people, you also might note how it explains the spotty service astropaths sometimes provide, I suppose.) worked over for a few decades. How do THESE psykers rise up to such positions of power, be they openly psykers who became "trusted?" Inquisitors, or Inquisitors who unlocked the power within themselves, in an organization known for trust issues, where one whole Ordo might want to kill them all? If your RT had children, and the heir-apparent displayed traits of psykerdom, I assume they'd have to be reported, and broken by the Astra Telepathica, also making picking up their inheritance later a potential impossibility. Why is this? If we ignore the power creep that can happen from psyker power, why can you play an Inquisitor who is, but not a Rogue Trader, and how might you? They aren't the same, I grant, but I often do view a lot of parallels between an Inquisitor, and a Rogue Trader.
Also, I am aware of the Awakened Psyker, in NP, and some of the Origin Path stuff that might get you a bit, but none of it is a psyker who has power; more just another character type with a one-off trick. I am not trying to just gripe about it, but the Inquisitor who is a psyker (Ascension), and also the Astropath Transcendent, have the ability to purchase more ranks in their power level, and more powers, to boot, while these "add-on options" usually don't. You might get PR 1, or 2, if you combine them, and a small assortment of tricks. I can see why you might not WANT this sort of BS in a character, but back to the question at hand, what's so different about the Inquisition and the RTs that one, and lets face it, the more nasty one, CAN have their highest-ranking members be openly potent, while the other has none, or people who must hide their middling power, unless they are a Chaos Sorcerer, to boot, in which case they must REALLY hide their power?