Integrated sucks. Proprietary integrated (ICBM) sucks worse.

Zero Stack (aka Internal or semi-integrated) is far superior to integrated due to the fact it uses pressed-in cups.

Zero Stack is nice for a couple of reasons.

Like Maelstrom stated, it can help reduce stack height.

A couple of product managers I've talked to say their instances of headtube ovalization has been severely reduced and eliminated after switching to Zero Stack headtubes.

Also, the larger headtube diameter provides more weldable surface. This allows stronger frame junctions and easier connections to oversized downtubes without relying on severe tube manipulation to pinch the end into a conforming shape.

I'd like to think given some of those benefits, Zero Stack is here to stay. With King on board with their slightly modified Perdido headset, even reluctant conventional holdouts don't have much to complain about (they just need to find a shop that has the reamer to oversize their ZS headtube the required amount).