Often you need not only to be at the higher level, but someone to call out that if they don't promote you you might leave. I've seen a lot cases (at many companies) where one person that everyone knows is good quitting for a promotion gets a dozen others promoted in the next few months. So if you realize you are not getting a promotion your leaving may be the trigger to get your coworkers promoted.
True, that can happen, but that feels toxic. A threat by the employee will always breed some negative feelings towards the employee, even if it is subconscious.
I am just writing about relatively sane, stable organization where the employer-employee relationship is stable and acceptable.
I think you (and the other) misunderstood. You are not threatening to leave here! Either you actually leave (their first notice is your two weeks), or someone else does and the company realizes if they don't promote good people fast those others will take the same hint and leave.
I agree that threatening to leave is a bad thing. Either get out or be content where you are: middle grounds do nobody any good.