How can the divs added by default by Views be removed?
On the contrary, you NEED to select the boxes for field, label and wrapper, and select None in the drop down menu. This will get rid of the &lt;div&gt;. 



The Add default classes has nothing to do with the HTML elements - only with the css classes it adds to the tag.  

Additionally you can deselect Provide default field wrappers under Format > Settings


EDIT: So, testing confirms that there are NO divs for fields anymore if you uncheck Provide default field wrappers. See image. Why modify a tpl file if you can do this with the interface? The only divs you see in the image are the ones that separate rows in the Unformatted list output. "See, mom, no divs!"