Happy to indulge!
I am just saying that once avijjā is eliminated, you are no longer dealing with DO. Yes, there are still all sorts of mental and physical processes going on, but they do not lead to rebirth and all that. DO is defunct.
What a word means depends on the cultural context. In ancient India every instance of birth was also an instance of rebirth. We don’t get this unless we render jāti as rebirth. It is important we try to understand the world as much as we can through the lense of ancient Indian culture.
Also, if you look at the four noble truths, the first one, dukkha, includes jāti. The purpose of the path is to overcome dukkha, which therefore includes overcoming jāti. The only birth we can overcome is future birth, that is, rebirth.
Moreover, there is another word that literally mean birth, namely vijāya. 