Plato Turns His Back on Orality?

We are all aware that the great philosopher Plato once criticized the use of writing, arguing that to use this new technology was to turn ones back on the oral tradition, to allow minds to become weaker since they were no longer required to remember so much since all of the information could be written down. The problem was that in order for Plato to argue his point to as many people as possible, it was necessary for him to write his arguements. We must wonder then if Plato's arguement actually did more harm than good. How could people take seriously an arguement ment to disuade them from writing that was itself written? Could he have perhaps shifted even more people towards the literary side of the arguement?