There are many reasons to call attention to things not working (e.g. the bottle example given above) and the ultimatum can be the last step. And when kids are involved (not in this case) it’s typically better for all concerned to have two parents if that’s possible. So you may hang in there longer than might look sensible from the outside.
Perhaps, maybe even probably — but what about two messed-up single-parent households?
In particular, textual flirting with the opposite sex is something that is easy to fall into, starting innocently and delivering a strong dopamine hit with each correspondence. The dopamine-addled S.O. can easily rationalize to themselves that they are just writing, that their privacy is suddenly Very Important, it's not cheating, and surely that's not innuendo! ("When we finally meet for coffee we'll just be friends.")
The well-delivered ultimatum, although blunt, makes the situation clear and leaves no room for rationalization: the emotions associated with the proto-affair are inappropriate to an exclusive relationship.
I've had to make this ultimatum twice. 50% of the time it has resulted in the recipient suddenly becoming self-aware and making an effort to change her behavior. As a result, I'm quite certain the current S.O. is not BPD.
"Give up the bottle, or I leave."
"Stop hitting the kids, or I call the cops."
(Other ultimatums, such as "Marry me or I kill the dog" are obviously abusive.)
In this case, the woman is forcing the man into a choice, but he still has a choice. "Show me that I'm not wasting my time or I leave" is in the grand scheme of things quite tame.