Use care when installing your licence plate on the rear of the car. The rear profile has a convex curve profile and an unprotected plate may damage your nice paint. Consider well placed felt or cushion pads onto the car first to isolate the potential for plate rubbing.
Good catch - sharp eye. I originally thought about putting felt onto the plate or frame as you also have. Much easier effort too. But with body motion / roll, the felt will be fixed solid to the plate but will want to move against the paint - with light dust and the slightest movement under the felt - light scuffing may occur on the paint. With pads adhered to the paint they will not move. The rear has dust there 1 mile after washing it. Likely it's not an issue for most anyways.