At this point the only way to add a class to an element on the page is to click on that element and move the mouse and click the Add Class Selector field in the styles pain.

I think it would be a lot easier to make a keyboard shortcut that opens the Add Class Selector field to quickly edit and add classes to selected element. Something like:

Shift + Alt + A opens the Add Class Selector field

This would let you immediately start typing the Class name without needing to move your mouse back up to the Add Class Selector field.