Because of large audiences! It allows meanings to be clear (assuming you know what the meanings of certain gestures are to begin with) and, for those packed theaters, allows those that are in the back to know exactly what's going on even if they can't see the expression on someone's face or make out what they are saying exactly! (Think: Shakespearean theater).
Of course, this is before mics and the invention of the proscenium theater and film and small intimate spaces. Is stylization so necessary now? Does it take away or add to a performance?
Rasa theory would certainly state that it's necessary, for more than the practical reasons. Rasa theory demands that one not delve too fully into a character or emote naturally because then you break down that fourth wall - the one where the audience and performers know that it is a play that is going on, an important aid in achieving a "spiritual high" when experiencing art.
However, currently, it is realistic acting that everyone is trying to achieve. Noh theater, bharatanatyam dancers, Shakespeare, Bollywood, etc: things that have been stylized for years and years are now making its way into the world of "realistic" acting. I wonder though that this is little more than the West's hegemony over the East. When stylization is scoffed upon and misunderstood by Western audiences as poor acting or performing, (I myself am guilty of this!) and Easterners are concerned with "being as good as the West", there seems little other reason for it.