You mean apart from all the times it doesn't?
There are countless amber zones, short adventures, merc tickets where off world forces - usually backed by megacorps - are subverting the Imperial recognised government.
The Imperium recognizes a member government until it changes, then it recognizes the next one. What government a member world chooses to have is, after all, an internal affair. Name three adventures, AZs, or merc tickets where the offworld organization is going for an outright takeover. There are numerous tickets where mercenary forces paid by offworld corporations are backing one local faction against the other. And practically every time the excuse for the small size of the forces involved is that the Imperium is preventing the corporation from furnishing more than that.
The only slight get out in your statement is the use of excessive force...
It's not a slight out, it's a crucial point. See below.
- but how do you define that exactly?
You don't define it exactly. The Imperium (presumably the local duke mostly) decides what is and what isn't too much.
"Excessive extraplanetary influence is even more vague. Historically, the Imperium has tolerated the use of force as an necessary outlet for built-up political and social pressure. In such cases, a short war is deemed preferable to continuing tension, sabotage, political agitation, etc. However, attempts by extraplanetary forces, such as offworld governments or large commercial interests, to seize control of a world's affairs is beyond the "safety valve" rationale.
"Assistance" is tolerated so long as it is deemed appropriate to the level of legitimate interest in the affairs of the world held by the extraplanetary organization. For example, the Imperium has often tolerated the provision by megacorporations of training cadre, arms, equipment, etc., on a limited scale, and even of training fully equipped striker units to local governments. However, when it has appeared that the primary burden for the conduct of the war has been carried by an extraplanetary power, the Imperium has intervened, claiming the power is using the misfortune of a local dispute as a pretext for aggression."
[MT:Imperial Encyclopedia, p. 28]
If you want to take over a world and are going to use private security contractors or your in house internal security division to do it by force you make sure that force is up to the job, which means overwhelming which could be interpreted as excessive buy the defenders while the Imperium looks the other way.
Any situation that would potentially lead to the world being effectively run from offworld would certainly be on the wrong side of the divide.
A local duke could collude with a megacorporation to look the other way, but I expect that this has been proven counterproductive. Presumably the ultimate result when one of the Emperor's hatchet-men arrive armed with an unlimited Imperial Warrant would be that the duke was replaced, the world was restored to local interests, and the megacorporation dleat a severe slap over the fingers.
[Hmm... that stirs a vague idea. As a result of some such shenanigans, a megacorporate subsector subsidiary gets confiscated and turned into a separate company, with all stock (except the Emperor's Share, of course) turned over to local interests. There ought to be some adventure potential there.]
But then, the Imperial family and local nobles often have shares in the megacorporations so its fairly obvious where their political loyalties will lie.
I've seen that logic expressed countless times, but it appears from the preponderance of the available evidence to be in error. The Imperium (which effectively means the Imperial family and the local dukes)
do curb the activities of the megacorporations. Regardless of their financial interests in those corporations they appear to have countervailing reasons that override them. Perhaps they feel an even greater interest in keeping the member worlds sweet.
Hans