My dad’s 69 Plymouth Fury did that, but then Mopars of the late 60s through the 70s were notoriously cheaply made cars. The 64 Ford Galaxie that preceded the Fury suffered no similar deterioration. Nor my aunt’s 70 AMC Ambassador, nor her 65 Fury that preceded it, nor my mom’s 72 Ford Gran Torino, nor my 70 Mercury Cougar.
Here is a door panel from a 64 Lincoln. The upper 80% of the door card is soft touch vinyl over foam. The bottom 20%, where people’s shoes scrape, is covered in the same carpet as the floor of the interior, so it won’t be scraped up. And there is a puddle light.