My take on the Psionic Suppressions is that they were forced on the Imperium from the bottom up.
We're told that there was an Imperium-wide psychohistorical experiment that went wrong (The entire Imperium?!? Hadn't these so-called scientists heard of control groups?). Exactly what the original aim of the experiment was, I'm not sure. It wasn't intended to drive everyone bat-shit paranoid about psionics, but what was it intended to do?
Be that as it may, the result was that all across the Imperium, from the Spinward Marches to the Solomani Rim, a groundswell of fear and hatred of psionics swept across the member worlds. And the Empress found herself scrambling to get in front of the parade and order them all to follow her. The suppression orders were one manifestation of this. I think there were other measures taken. Something like an Imperial edict directing the individual duchies "to enact such legislation as is necessary to solve the Psionics Problem" perhaps.
But the problem (and the legislation) started at the level of the member worlds and the Imperium jumped on the band-waggon because otherwise it would have faced problems with the member worlds for being "soft on Psionics".
The way the Imperium is set up, the only way I could see it happening Imperium-wide is either Imperial edict, or psychohistorical experiment. Information travels very slowly in the Imperium, and it remains a pretty culturally diverse entity. If one looks at it memetically, any meme that did not have a universal trait for survival could not infect even the majority of the Imperial population, let alone nearly all of it. For it to be a spontaneous groundswell, it would have to appeal to some psychological aspect that was common to every world in the Imperium (or very close to every one), and given that cultural diversity, there wouldn't be many. But even if this was true, then the issue would be timing: why then? If it was so universal, why didn't it occur earlier? What changed? There had to be some catalyst to "set it off", whether it be events (like the Frontier Wars), or some tragedy (like what started the Sudusham Concords). So what could that trigger have been? I can't see any trait universal to all human cultures changing, so it had to be something else, something external. So there are two questions that need answering in order for the spontaneous groundswell theory to work.
And anti-Zho doesn't cut it, since most of the Imperium is too far away from Zho space, and one would see a sharp drop in anti-psionic sentiment the farther one gets. One might surmise that the Solomani would embrace psionics as a way to get an advantage over the Impies, even if only unofficially. In that case, SolSec would become a lot like the Psi Corps from B5, because you know they'd use it if they could, so why don't they?
Imperial edict works because they were the ones at war with the Zhos, so they could spread it across the Imperium. However what you said about member worlds feeling interfered with would have indeed caused a problem. The Imperium's jurisdiction is supposed to cover interstellar space and, to a lesser degree, the rights of sophonts, so I don't see how they could get away with this without popular support beforehand. So a psychohistorical experiment would seem the elegant solution. And sure they could have used control groups, but containing a meme can be like containing a virus, and a single leak can result in a widespread infection pattern. It could also explain why the Solomani still embrace this idea, despite the obvious advantages: they are simply still infected.
