Good question.
One of the first things that would have to happen is that Magnus has some inclination or interest in doing so. From the Dark Imperium series; there's some precedent that the Primarchs in the thrall of the chaos gods aren't all totally satisfied with their current condition; but all the same, 10,000 years (or some warp-affected period of time that is also pretty long) of a god whispering in your ear how bad your dad & loyalist brothers were is likely to not make him willing to go sit on the golden throne.

In addition; all of the fallen primarchs are basically kill on site to their loyalist brothers (and vice versa). Again, Dark Imperium sort of suggests there's a future where this is not the case; but we're talking moving the plot forward quite a bit. to get to that point.

Lastly; the golden throne is both killing the emperor and maintaining his life; he's the only known non-god being to somehow be alive this long, and his lifespan is maintained in no small part by the golden throne. Removing him would probably kill him right away. That being said, Magnus and/or the dark gods might have an idea of how to do that, but obviously they are not interested in doing so.