Except that really the reason that Astropaths have their reach has nothing really to do with their personal power; it has to do with their soul bond to the Emperor.
To quote Lexicanum:
In fact, after the ritual they are linked to the Emperor and their new abilities are a result of the combination of their powers with a fraction of the Emperor's.
So no, it's explicit that their abilities
are reliant on their personal powers, and it's a
fraction of the Emperor's, a description at odds with the "Switchboard" analogy. Though in line with the communcation blackout from the Astronomicon blacking out. Also, this ritual is done at the
end of Astropath training, which is important given Wyrdvane Psykers.
And no, virtually all human psykers are soul bound. For a human psyker to be sanctioned and not soulbound makes them basically a one in a billion psyker; and most of them are snapped up by the Inquisition.
To quote Lexicanum (again):
Astropaths are psykers collected by the Imperium's Black Ships whose powers are considerable, but who lack the mental strength to resist the dangers of the Warp.
They are selected because of a
particularly high-power, high-risk potential, while the battlefield psykers are constantly watched by Commisars, with the site having the following to say about the fully-trained Primaris Psykers:
Due to the constant risks of daemonic possession, a Primaris Psyker's wargear also includes several fail-safes. Complete micro-circuitry and neuro-active wiring are connected to the psychically attuned crystals embedded in the psyker's hood or collar, designed to bleed away excess Warp energy. These, coupled with cranial surgeries undergone by the psyker to implant neural inhibitors (which tend to blunt the psyker's innate power as well), and a lifetime of training, give the psyker a reasonable chance at avoiding powerful psychic enemies and resisting daemonic influences.
There's a clear separation made between Soul-Binding and Psychic Hoods (or at least whatever related technology the Primaris Psykers are using), and combat psykers are known to be fielding in squads that
aren't fully trained and rely fully on combat-groups reinforcing eachother, known as Wyrdvane Psykers:
Wyrdvane Psykers are Imperial Psykers of the Adeptus Astra Telepathica's Scholastica Psykana that are not able to control their powers. Some have not yet completed the grueling training to become a Primaris Psyker. Others will never achieve that goal, introverted beyond rescue by the horrors of their own minds. As individuals, such psykers are unpredictable and unsafe. Yet working in concert, these deadly mutants can be a valuable asset. Attuned to one another, Wyrdvane Psykers draw strength from communion. Squads of Wyrdvanes link their thoughts to strengthen each others powers.
You may be mistaken because it's the same organization doing the training, you're relying on some Black Library source I haven't heard of and Lexicanum hasn't included, or Lexicanum and the other secondhand sources I've read haven't updated from more recent codexes contradicting its current information. Can
very easily be the last, the source used for most of this on Lexicanum is Rogue Trader era material. Also, I
did intentionally prune the links from the text I quoted, but I just pulled it out of the pages for "Astropath", "Sanctioned Psyker" and "Primaris Psyker."
Basically, from what I've read (which is overwhelmingly second-hand information.), there's at least two tracks for Psykers, of which Astropaths are selected from high-risk individuals to whom Soul-Binding is deemed most necessary, while the solo-combat Primaris Psykers seconded to the Imperial Guard have a number of indications of being the conclusion of a different training program, including a separate method of reducing the risk of possession, with those who haven't finished that track of training still being fielded.
And Wyrdvane Psykers in particular are cited as being mentioned on page 70 of the 8th edition Codex: Astra Militarum and were (seemingly, as it's the earliest cite for them) introduced in 6th edition, so
those explicitly-incompletely-trained battle-psykers are modern lore.
A further contradiction to the notion of all Sanctioned Psykers being Soulbound, and additional Lexicanum page (this time being for the Scholastia Psykana, the organization that does the actual training, itself):
The first ranking of pskyers (referred to as primary psykers) are those whose powers and strength of character are sufficient to resist possession and daemonic corruption under normal circumstances, and are chosen to serve the Imperium in the highest capacities. After receiving five years of basic training at the Scholastia, they are sent for further training and service in another Imperial organization depending on where their abilities are judged best suited. The very young may be indoctrinated into the Space Marines as Librarians; some may enter the Imperial Guard to begin their training as Primaris battle-psykers; the most talented may become Inquisitors or Grey Knights.
The majority of the discovered psykers form the second ranking of psykers. They are trained for service as Astropaths (i.e. astro-telepaths), psykers specialised in interstellar communication, being able to send and receive telepathic messages over vast distances. The Astropaths perform one of the vital tasks in the Imperium; psychic communications is the only practical means of communications in the galaxy-spanning Imperium. Some primary and secondary ranking psykers are given over to the Adeptus Astronomica, a smaller organization in which the psychic recruits continue their training.
Astropaths are
more common and selected based on
not being able to resist corruption under typical conditions, but aren't the sanctioned battlefield Psykers, of whom the higher-power outliers are a major source of Librarians and Grey Knights.
Navigators aren't really psykers at all though. Oh, they interact with the Warp but they do so in a manner far different from a psyker.
Hence singling them out as the only major demographic of "Bleedthrough" Psykers, those who's Psychic potential is
primarily in realspace, and thus having relatively limited access to more typical Psykana or Sorcery. It's a headcanon of a three-axis system of Psychic talent that the primary measurement method used detects the aggregate of, with different axes covering different elements of what it means to be a "Psyker".
It covers personal power without active use of channeling from the Warp, the distinction between this and presence of Psychic phenomena despite separations from the Warp, and the fact that Sorcery is often distinct from active Psyker abilities, despite both being Psychic phenomena generally considered to be drawing from the Warp.
It's a headcanon. A belief on the setting given the nature of what I know about it, extrapolating from facts known to me and now backed by (or rather not contradicted by) the wiki. If you have contradictory citations, please do share where they may be found. And put it in the Lexicanum talk pages, if not outright doing the editing yourself, to keep Lexicanum updated on the lore.