I think you're mixing up Xavi's and Iniesta's roles. Iniesta always had the tendency to go up when on the ball. In fact, this is the reason Iniesta's game suffered under Lucho a lot of times, because his role has been changed into a CM with more defensive duties, while his natural abilty is that of an attacking midfielder.
Even for Spain, Iniesta was an attacking midfielder, with Xavi being CM, and Xabi Alonso and Busi being a DLP/DM double pivot.
Iniesta is a CM, by being a CM you tend to be hybrid. You can play more defensively (DM-like) and more attacking (CAM-like)
Just look at the players i mentioned in Set 2 as CMs you can play them beside a DM and as a CAM without a problem
But try playing players in Set 1 deeper and you will see hell run loose.
So his ability to attack as a CM is fine, Verratti plays very deep for PSG for example but when he goes up it's a key pass or a dribble. CMs tend to be versatile but CAMs nahh
That is why with Iniesta. There were times with Rjikaard he played very deep, with Pep he played further forward because we had Xavi and Iniesta
And with Lucho he plays deeper because we need his CM abilities there
This is something you can't do with Coutinho, Ozil. You either have them play closer to goal where they can score or assist, otherwise they are dead
For Spain Iniesta had to be a CAM, you have two DMs in Xabi and Busquets and a playmaker. He had to be given attacking duties
But his natural position doesnt change. He's a CM