Cleaning up the plastic reels after each use takes about 15 seconds. Split the reels apart and quickly swirl with a dish brush in warm water. When done every time, this is enough to prevent final rinse agents from accumulating. If you still find it is insufficient, a more thorough cleaning once a year or so may help.
So, this is not a very good reason to turn to stainless steel reels. It's more a matter of taste if anything.