I did a number of experiments earlier this summer. Deactivate and reactivate Climate and/or COP, unlock and lock remotely, open the tailgate remotely and close again etc. I could find no way to reset the 12-hour time-out for COP by using the app. The only method that works is that I go out to the car very late at night (early a.m. usually), open the door for a few seconds and close it again. Then, the car keeps COP active for another 12 hours. I usually inquire of the Tessie Control skill through my Alexa (Echo) devices to verify yhat the daytime cabin temperature is running around 100°, and then again to turn on full Climate A/C some minutes before I expect to drive out somewhere.
There have been some rumors of upcoming COP enhancements. I'm hoping this includes better remote app control for extending the time limit and or adjusting the COP temperature, though for me the 100° setting is a pretty good one.
It's very true that my other cars get super-hot and simply aren't monitored the way the Tesla is. It's also true that these cars suffer interior aging year by year, and to me it's a fantastic feature that I could prevent this from happening in my Tesla. So to me, whether or not the original design intent of COP was to protect the car vs the survivability or comfort of occupants, I do find COP extrenely useful to protect the car.