It’s been a long time since the last time I rented a car but I used to rent cars to date girls who lives out of town.
I used to take out the extra insurance because I was told that no matter what happened I could just return the keys and be off the hook. If I used the insurance supplied by the CC it would be my responsibility to fight it out with them if there were any issues in the fine print.
There was one time it came in handy, I stopped at a rest area and when I came out the whole drivers side was smashed in. There were no notes left or anything. I made sure the girl never saw that side of the car (didn’t help- she said no anyway) and let the rental place know about it the next morning. The only thing they wanted to know is if everyone is OK.
On the other hand I only rented the car for one day at a time- if you are renting for a week or more the extra $25 can really add up.