Here is my thought on this.
Ultimatums (if you drink again, we're through) put the power in the other persons hands. They are a manipulation technique. We are hoping we won't have to take responsibility for ourselves, so we hand it over to them, keeping our fingers crossed that they will choose to take care of us.
It very often backfires, and often does not accomplish anything more than us having to eat crow, and them realizing we don't mean it.
We, at some point, have to use the power we have in our own lives, to make a change.
Saying, "I won't be with you when you drink" and then not being with them when they drink, is us taking responsibility. We say what we will do, and don't try to get them to do what we hope for.
"I'm leaving. I will not be with a drunk" is a strong statement. Saying it outloud, taking ownership of it makes our stand clear to ourselves as well as them. They can do whatever they are going to do, but we are not going to be with a drunk, period.
I know this is easier said than done, especially when there are finances, kids and a lot of time invested in the relationship. But it is what we work towards.