Photos app's import keeps finding already imported images from an iPhone...

There are several possible reasons. The most common reason is a format conversion from HEIC to JPEG. Please check the Settings on your iPhone:

• If your iPhone is set to take the photos in the High Efficiency format, but you are converting the images to JPEG on Import, the remaining HEIC files on the iPhone will always appear as new photos.
  • Check "Settings > Camera > Formats". is this set to High Efficiency?
  • Check "Settings > Photos > Transfer to Mac or PC". Is "Automatic" enabled? Then set it to "Keep Originals" to avoid the conversion to JPEG.
• Other possible reasons are related to iCloud. You wrote that iCloud is not enabled, but check, if iCloud Photos, Shared Albums, My Photo Stream are really turned off on the iPhone. iCloud Photos could become enabled by default after a system upgrade, without you being aware of it.
• If you manually sync photos to your iPhone, they may appear as new photos, if you add adjustments to them, because this save a new copy to the camera roll.
• Are you using WhatsApp? I am not using it, but some users reported, that downloads from WhatsApp will continually appear as new photos. Then ask in the iPhone forum, if there is a fix, perhaps reinstalling the most recent version of WhatsApp.

Thank you. I will check the settings as you suggest. However, the multiple replications seem to happen most when importing photos from scanned images or other cameras' photo formats, not from images taken with the iPhone. The idea that the image is assumed to be "new" each time one opens the Photos app is interesting, but I still don't know how that can be remedied. Also, since Apple warns that third party software meant to find and remove duplicates can be dangerous, why does not Apple have a system to identify and remove duplicates? Martin