Astropaths, as far as I've always thought, have always been a mainstay of Human communication. The thing about Astropathy is that it's not an exact science. A message can be caught in the warp for a long time, or it might be received before it's sent. There's just no telling. Also, as an Astropath is basically trying to interpret a message that comes to them very much like a dream, it might be that working out what the message says takes a lot of the time.
As for news of the Heresy spreading slowly, as has been mentioned the warp was incredibly turbulent. Just as Imperial starships require a calm warp, or at least stable warp currents, to be able to actually get anywhere, so Astropathic messages are jumbled, delayed and lost in the warp storms. At this point couriers are more necessary, but then the turbulent warp delays them a well; at least if they get where they're going the message doesn't need interpreting!
I suppose what I'm trying to say is that the warp, and its use, is the backbone of Human mastery of the galaxy. Interfere with the warp, make it violent and implassable, and you hamstring the Humanity's ability to communicate with itself and to move its forces to where they need to be.
The warp storms surrounding the gestation and immediately before the birth of Slaanesh are what curtailed Humanity's first great Empire. No messages or ships could get through, the storms clearing intermittently and at huge intervals for only tiny periods of time. This is why the first Empire split, as it couldn't administer such a large area without comms and military/humanitarian support.
TL;DR the warp and Astropathy (to my mind) has always been indispensable to Humanity as it's the only way that communications can span galactic scales in anything like a useful timeframe.
Did I actually make any point there at all, or did I just ramble on and waste everyone's life?