@Aethelwine, I am in no way challenging your premise here, but my perspective is very different from yours, perhaps because I am a chunk older than you and my experience differs.
In my world, the main reason to give an ultimatum is not about claiming power at all, but to primarily inform of a circumstance/attitude/behavior that is so egregious (in my perception) that it must be addressed, or I can no longer be part of the relationship.
Here are a couple of examples:
Like @MrGrimm888, substance abuse is a deal breaker for me.
Lack of respect for me, as evidenced by constant, unapologetic lateness has been another. I’m talking about the kind of repeated lateness where I have waited a long time, without any word, to find out the next day that the person “decided” to do something else.
As I have gotten older, I have also really re-defined my idea of “true” friend. I know that a lot goes on that I don’t know about in others’ lives, and I no longer expect uncondonditional support from anybody. If someone I consider to be a true friend gives me an ultimatum, I consider it very carefully and try to respect the reasons they might have. I don’t necessarily comply, but I try to understand how we got to that place.