I don't know which he like: tethered battery or heavier headset

Steve wanted Jony Ive to have final say, and Jony Ive wanted the product to be fully mobile. I don't think that the wire will be present in version 4+ of the product

I don't think Tim Cook likes the battery brick more than Steve would have, but there are engineering compromises to make here.

maybe if it doubled as an input device

I like this idea, but how or what? The power brick is obviously critical, but I'm guessing they want you to put it in your pocket or on the desk or bed/sofa and largely forget it's there?

The demo of Vision Pro shows a virtual keyboard for a bit. That means it supports gestures (with hands and eyes) and typing on the keyboard.

If only Apple made a device in a similar form factor...