No there is no universal cookie dough base. Otherwise all the cookies would taste the same. What gives a cookie it’s unique flavors and textures is the differences in the percentages of ingredients to flour.
Shortbread is shortbread because it only contains flour, butter, sugar, salt, and for those wanting a melt in your mouth shortbread cornstarch; rice flours those wanting a sandy, crunchy shortbread. The ratio of flour to butter can be as high as 100%. There’s no chemical
Chocolate chip cookie is created with a completely different ingredients which include baking soda, brown sugar, egg, and vanilla extract.