I recorded what I think I will use as my main Zoom set up so that I could see (an approximation of) what it will look like for students. If you are a member of the HFC community you can watch it, too. If not then you will not get much at all from this post.
The result: On an iPhone the screen size required higher than a 12-point font. It worked with pinch zoom, but pinch zoom does not hold (at least on videos) if you release so zooming in is essentially a requirement.
Likewise, when just the document camera view was showing switching to portrait allowed a pinch zoom that allowed more screen real estate. However, it did not hold. So there is no advantage using the recording for a single window. However, pinch zoom does hold on an iPhone when using Zoom (I was multi-tasking just now so I could check) so there is some advantage when not needing to project anything other than what you are writing.