We know (If I recall correctly) that the Emperor planned for Magnus to take his place on the Astronomicon and the Golden Throne.
The Emperor planned for Magnus to sit the Golden Throne in order to power/protect the man-made section of the Imperial webway (the Thrones original and primary purpose). The Astronomicon is simply a by-product of the Emperor, his soul-light reflected in the warp. These days it is primarily powered by the thousands of souls sacrificed daily for it.
I think that it appears that Lorgar may have had the latent power to do this but I'm not sure of the others.
I think (and this is purely speculation) that sitting the Throne is more a matter of control than raw power. That being the case Lorgar's untapped power isn't going to be that useful and neither are any of the other Primarchs more latent abilities.
Since the Primarchs weren't immortal, I wonder what was the Emperor planning to do when Magnus died and could no longer direct the Astronomicon?
1) Mentioned above, Magnus was never supposed to direct the Astronomicon.
2) We can't actually say whether or not the Primarchs are immortal. They aren't invincible (they can be killed) but we haven't actually seen a single one die of old age, or even show signs of aging. Sitting on the Golden Throne is probably the safest job Magnus' ever had so he's not likely to die a bloody death doing it, meaning that it's possible he could've done it forever (though he'd get really, really, really fucking bored).
Interesting thought about Horus. What makes you think he was powerful enough to direct the Astronomicon?
Horus was powerful enough to go toe to toe with the Emperor it's certainly possible that he's as powerful in other aspects.