IPhone – Mac usually can’t read data from iPhone over USB

I have an iPhone 6 Plus and a 2015 MBP. Both are running the latest OS.

My goal is to transfer photos from the phone to my Mac. I've been able to do it before. But now, here are the symptoms:

1. When I connect the phone to the Mac, the Photos Import program immediately displays "Philip's iPhone" in the Import section.
2. When I click "Philip's iPhone", Photos Import sits with a blank screen for 2–10 seconds, then pops up a dialog box that I need to unlock the phone, and the phone prompts me to Trust the computer. I click Trust.
3. Photos Import continues showing "No Photos".

Meanwhile, I have iTunes open. Once I go through the above steps, iTunes pops up one of two messages: "Could not read from the device" or "Could not send a message to the device". There is no phone icon in the top-left corner of the iTunes window. Closing iTunes has no effect on the steps above.

Once today the Photos Import app actually showed my photos, and I was able to import half of them until the transfer suddenly stopped. I was holding the phone in my hand at the time, so maybe something is physically loose. However, jiggling the cable hasn't helped.

I've tried several cables and both USB ports on the Mac, without any change in behavior.

I am mystified. Suggestions?