So strangely enough video made for Gourilla Collective has slightly different choice of game footage.
https://youtu.be/K1EokJQ_HpI?t=159Here, the roll is clearly between Allies and Enemies.
My preference for team turn, rather then character turn comes mostly from complexity of interactions it brings - I find that ability to choose what moves with whoom I do first bring another layer of gameplay which I enjoy - having individual initiated I feel, flattens things a bit.
I hear you regarding the danger of alpha striking - if whoever is starting gives a massive advantage (like in FiraXCOMs) that can be greatly detrimental to overall experience - whenever it is in favour of the player or not.
However, I think one can get around it in many different ways without reverting to individual initiative. For one, I wouldn't necessary refer to table-top balance - Larian is making changes to DnD, so I trust that with change to initiative, there also comes a change to balance. I also thought that turn-based mod for Pathfinder: Kingmaker had a right idea - initiating party didn't get to make a full turn - so while it is an advantage it's not a crushing one: winning party can dish out some damage if they are in range but a lot of initiation comes with ability to set up, rather then strike.