I agree fully that astropaths, and maybe other non-sacrifices are brought in close proximity to the Emperor. It's more a question of what constitutes close proximity to an entity whose soul is visible to something like 7/8ths of the galaxy.

In my own personal version of the Imperium things like the Black Ships taking a century to complete their routes is mitigated by having numerous Black Ships having over lapping routes. A Hive world is probably visited every year or so, where as a backwater colony with barely ten thousand people may only see them once a century. Same with things like having only a handful of Forge Worlds provide most of the high tech things, any world with a reasonable AdMech presence will be producing high tech gear, just nowhere near the same output or some of the more esoteric things like Titans, or land raiders or the like.

Alasseo said:

You good sir, have made my day with this image.

2 pieces of robot for you! (Not really-kinda like a provincial meme)

I have reasons to believe that Astropaths do not enter into the throne room and witness the emperor when they are soul-bound.

in Blood of Martyrs it says that in the Reign of Blood (millennia 36) the Custodes general finds Alicia Dominica (the leader of the Brides of the Emperor/Daughters of the Emperor) and ask her to enter the throne room with him and witness the Emperor and there the truth of would be presented to her.

It says and I quote (page 13):

"The Captain-General made an impassioned plea for the Brides of the Emperor to see the truth of the regime they served. Though he spoke for many hours, Alicia was unmoved, for her oaths of fealty were such that she could never renounce her master. Then, the Centurion made one last appeal. He asked the leader of the Brides of the Emperor go with him to the very heart of the Emperor's Palace, to the long sealed throne room itself, the most holy place in the entire galaxy, where the truth would be revealed to her. The leader agreed."

Then later that page:

"The Captain General issued the six Brides of the Emperor the direst of warnings. they were told that to speak in the presence of the Golden Throne would be to invite death. At his order, the mighty doors opened for the first time in millennia, and the group walked into the golden radiance shining forth"

So if the doors to the throne room had been sealed since millennia 31 to 36 and Astropaths needed to be brought before the Emperor, there would have been no Astropaths for 5 millennia, which seem highly unlikely.

Rex Tauron said:

True, but the advantage of psychic senses is that they're not strictly limited by the physical spaces the psyker is within. The would-be Astropaths don't necessarily need to enter the Throne Room to "witness the Emperor". There's probably a chunk of the Imperial Palace controlled by the Adeptus Astra Telepathica for Soul-Binding, Sanctioning and so forth.