What is the purpose of baking soda in chocolate-chip cookies?
Baking soda also raises the PH of the product resulting in better browning.

Soda can be left out. Many recipes- especially for chewier cookies- don't call for any leavening besides the eggs.
http://www.foodnetwork.com/recipes/alton-brown/the-chewy-recipe/index.html

Cookie recipes often call for the dough to be chilled so that it spreads less in the oven before it sets. This creates a taller, less crispy cookie. Cookie recipes don't typically have very much water in them for the soda to dissolve into. Much of the water is tied up in the butter and won't be available until the dough melts in the oven.