The dead branch was coming out of a split. None of my usual clippers could get in there to make a clean cut flush with the trunk I was keeping so I wound up having to shave away material to get a clean and close cut. I have been told that this is the thing that concave cutters eliminate.
There are many ways to do this, and it seems you found your own way - by shaving away material. I do that too, occasionally. If my concave cutter or my knob cutter do not suffice (for example, when the branch is too thick for the cutter) I use a dremel to carve away material.
What I am trying to say is that each tool has its specific purpose - but the only tools I find absolutely essential are bonsai sheers.