Why does live photo persist. I want it removed from my machines It is a waste of space and TIME!!!

It’s like Old Toad said. The iPhone defaults to live photos. So if you turn it off for one photo it will reactivate for the next session. To deactivate live photos permanently you must deactivate it for the present session and then go to iPhone Settings/Camera and preserve the Live Photo sertting that you just made, that is, to turn it off.

— Rich

Is the problem, that already deleted Live Photos keep reappearing? Or that the Camera is reverting to taking Live Photos?

If already deleted photos keep reappearing, you may want to check the sharing options you have enabled, depending on your system version. Are you using the Shared iCloud Photos Library? Could the photo have been shared from Messages?

Delete it from your iPhone and Mac. When you take photos with your iPhone make sure you don't have the Live feature activated.