I didn't use to until I had a rubber rim strip literally decompose inside the tire. The bike had gone unused for a while. of course got a flat 12 miles from home, the majority of the rim strip came out with the tube. Pieced together what I could of the strip, put in my spare tube and just made it home before it flatted again.
Picked up a gallon size zip lock bag of velox rim tape at a swap meet. No more rubber strips.