This bothers me. Possibly my fluff is out of date, but I don't recall the Adeptus Astra Telepathica being the body of all the Imperium's psykers. I remember it as being exclusively the structure of Astropaths. I mean assorted clerks and support staff, etc. But essentially it was the Astropaths. Imperial Guard psykers or anywhere else sanctioned psykers might end up, were not part of this adeptus.
So fluff-wise, this grates just because of that. However, further to this, is the fact that any psyker from any other background will be unsanctioned! Now you might get the more radical Inquisitors occasionally making use of an unsanctioned psyker at their own discretion... just conceivably. But as a pretty good rule, unsanctioned psykers are a pretty big no no as I have always understood it. Along the lines of "thou shalt not suffer a witch to live". If you find one, you either kill it or pack it off on the Black Ships where it belongs (assuming the ships are available).
I would like the option of playing an unsanctioned psyker, sure, but I don't want to have to pick a particular background not to be one. Unsanctioned could easily be implemented as an option. You could even give a small bonus in some way to represent their untamedness if you want to compensate for the huge amount of trouble they may face. But that's secondary. It seems to me that Sanctioning should come as standard for any PC psyker.
That's my thoughts. It just seems weird and constraining to me to have one set background (in practical terms) for psykers when I can easily make holy Warriors from a Ministorum background (like the Sisters of Battle) or assassins from an Imperial Guard background (like scouts) or Sages from Adeptus Arbites (lawyers or strategists) or a Seeker from an Arbites background (a detective) or from an Outcast background (a bounty-hunter or smuggler). Lots of variety. Except for psykers. Make them sanctioned by default and then let them pick backgrounds as they choose!