From the second Letter from the Producer Live:

Q: Will new players who start playing after 2.0 get to experience the current main scenario? Also do they get to challenge instanced raids and primal battles that are available now?
A: First of all, please be aware that the main scenario and the Seventh Umbral Era aren't really the same thing. Players who start after 2.0 should be able to experience the former.

Regarding instanced raids, they will basically remain as it is and they'll be carried over to 2.0. Now with the primal battles, some plots are connected with the Seventh Umbral Era. I say that there is a good chance their appearance may change in 2.0. Some will remain the same, some won't. So basically, the current game balance and the current reward will only be available now. Some of those items already exist.
I'm pretty sure the removal of the achievements for the primal fights means the battles, as they are today, are going away. For all we know, the primals might reappear as part of the Summoner's AF gear quest line, where every 5 levels you fight another primal for access to it's abilities. So, they won't disappear completely, but we want be able to fight those three after 15 minutes.

Which makes sense as you only get the primal achievements for defeating them in hard mode and not in their easy form.