Re: learning to throw from both sides at once, my instructor stresses that primarily because he has an actual muscle and posture imbalance due to prolonged heavy favoritism of one side his entire life. However, maintaining this might arguably as easily fit the category of learning both sides but not at the same time.
Also, I question whether this would be an issue with a steady and intelligently designed strength training program outside of judo.
"Use what talents you possess: the woods would be very silent if no birds sang there except those that sang best." —Henry Van Dyke