Answer:  

Mr. Shinichi Takagi, who is actually studying eggs, kindly answered the question above.
 
  
Is it better not to over-stir the eggs? 
When you pan-fry the eggs, it's better to avoid over-stirring as you have commented above. In contrast, when you want to prepare the dishes like Chawan-mushi (pot-steamed hotchpotch) or egg-tofu by steaming the eggs, you must stir them well to make a homogeneous egg liquid; however, it is better not to create foam in the liquid.
 
Now, let me explain to you why it's better not to stir much when pan-frying the eggs.  An egg has both egg yolk and egg white and each part has its own texture (egg white has jelly-like and egg yolk has rich creamy texture). When the eggs are stirred well and the liquid becomes almost homogeneous, palatable textures of egg white and egg yolk will be lost and becomes dull. Therefore, in order to enjoy the harmony of the texture of each part, it's better not to stir much.
 
Especially, when you cook some dishes like Oyako-don (bowl of rice topped with chicken and egg), it is crucial that you do not over-stir the egg, or neither taste nor appearance would be appealing.  There are some liquidized eggs on the market: The "liquid egg", which has been on the market for some time, is a homogeneous liquid that has been filtered and sterilized. In fact, there is a new product called "twin pack liquid egg" in which egg white and egg yolk are separated to be used in particular dishes such as Oyako-don and Katsu-don. 

The following are the three major characteristics of the eggs: 
 
1. Coagulation
Eggs are coagulated when they are heated. Some examples of this property are fried eggs and boiled eggs. 
 
2. Foaming 
When you beat the egg white for a few minutes, it starts to rise by creating many tiny foam bubbles. Some examples of this property are meringues and sponge cakes.
 
3. Emulsification 
This is the key procedure for preparing creamy products such as mayonnaise and ice cream. Emulsification is a mixture of two liquids that are originally incompatible by letting one of the liquids disperse into the other liquid as tiny particles. The emulsified liquid is called emulsion. The smaller the size of the mixed particles, the easier for the substances to be emulsified with other liquids.  Particularly, the egg yolks are emulsified very well, and they can be emulsified four times more than the egg whites.  Milk, margarine, and salad dressings are also emulsions.
 
 
Acknowledgement
Mr. Shinichi Takagi
He is managing the website “egg museum” which contains a lot of information about eggs.

This article is translated by Chemistryquestion.com from the original article in Chemistryquestion.jp.  Please let us know if you find any errors.