The Verdict

A walk in Old Town gave me an opportunity to try out the new phone grip.  The generous size of the images from the iPhone 14 allows for a lot of cropping, so the end results don't look much different than from those made with the naked phone.  However, I found the grip to produce a much more familiar and comfortable shooting experience. 

Carrying the phone with the grip also encouraged me to use the phone camera in a more sustained exploratory manner, so that instead of one or two targets of opportunity I ended up engaging with a variety of subjects.

A big plus for the grip is that it provides  much more steadiness, leading to more carefully framed compositions and a much better chance of level horizons and upright verticals.

So, a more satisfying experience in using the iPhone for photography, but not without some compromises compared to shooting a real camera.  Activating the shutter release and the zoom with the bluetooth connection produces a small time lag, so capturing action is a bit of a challenge.  My experience with using the phone camera is very limited, so I may have more to say about that and other issues down the road.  Meanwhile, I feel at this point that the small cost of the grip has been a good investment.