I'd say the real problem is not the tool itself (finger counting, in this case) but a stubborn reliance on that tool even when it obviously can't scale. Some of these students were more concerned with just executing the algorithm than understanding process of addition, and consequently, some struggled with multi-digit addition, negative numbers, fractions, and so on. They coped with their inability to solve more complicated problems simply by not ever attempting to do the work. The attitude was "I don't get it immediately so I'm not even going to attempt to understand it".

I'm really not trying to bash the students. As a teacher, my job was to invest the students in wanting to learn, and I admittedly wasn't always effective.