and the later robust type, Australopithecus robustus, which became extinct

Well then it wasn't very robust, was it? Hopefully our self-made climate change won't prove too catastrophic and make our "wise wise" epithet the butt of some future species' joke!

Larger brains and more dexterous hands probably encouraged the increasing use of tools as well as innovations and refinement in the production of tools.

I think it might be the other way around. Nature selected use of tools (because it was beneficial for survival), and use of tools was associated with (caused by?) larger brains, so the brains got dragged along.