I think this can be seen more generally - how does any non-Imperial faction maintain long distance communication?
Obviously many aliens have their excuses - Eldar have the webway and frakking powerful psykers, Necrons are hugely technologically advanced and Orks wouldn't really care.
For Chaos, we can easily argue the warp did it, but the interesting one is pre-Imperial human civilisation. Although the Emperor has been around since about the 9th Millennium BCE, he wasn't exactly making himself known at the time.
My guess? Ruling out there being some manner (forbidden or otherwise) of producing a poor man's substitute for an astropath, its possibly it's simply a case of post riders.
It wasn't until the introduction of semaphore networks in the late 18th century that complex messages could start to travel long distances significantly faster than a human. (But even so, it wasn't really until the electrical telegraph that things really became practical. Semaphore doesn't work without line of sight, so no communicating across the Atlantic, sending messages at night or in bad weather). Significant human empires nonetheless predate this time - Genghis Khan, Alexander, the Romans, etc.
Now, obviously, astropathic messages have a speed advantage (and they're much harder to intercept) which would give the Imperium a notable benefit when planning a war... but to be fair, when planning a war on a segmentum level, if you're not playing several months ahead anyway, your troops probably aren't going to be in the right place regardless.