My vote is yes.
My opinion on how to accomplish this without over-burdening the Factory and Role-Play Judges is to take advantage of what we already have in place. Right now, we have a guide that explicitly states how to grow in tier. And we have a template/standards that limit the amount of locations and operations a company can have at submission.
(That said, I preface this suggestion by pointing out that tier demotion strikes me as a PvP sort of thing. Unless major events transpire where demotion makes sense i.e. CEC and Brokellia, then I foresee tier demotion being a thing that other players strive to do to other companies.)
A potential system would simply make use of the company modification thread and would rely upon other players to accomplish. You would have two "types" of demotions. One would be General Stagnation, and the other would be "I Stomped Them".
With Stagnation, a player does the investigating. The company has to be inactive by the same standards as Canon company inactivity and must be proven, in detail, by the player. (Aka, last submission, last IC company post). Once provided, the player requests the appropriate tier demotion for the company and the Factory staff treats it like any other submission modification.
In the case of "I Stomped It", require that corporate assaults with the intention of yielding a tier demotion must occur exclusively using the Skirmish tag (or something). Require that the player adequately tag the company owned being attacked, etc. These threads can be basic hostile takeovers, BDZs, whatever. But once the dust settles, the player then requests the submission modification and links the successful skirmish in their request.
We leave the degree of demotion up to the Factory staff, based upon the level of effort in the stomp threads or severity of inactivity.
Through these, we aren't relying upon the staff to do all the work. The players are involved and are doing the grunt work. The Judges are simply taking a gander at singular, submission modification requests.