If I have a tool box, I'd really like for tools to automatically go there when they come into my inventory, just like spices do to the spice rack or other items do to bags assigned to that item type.
Far as I'm aware, they already do. Every Random Kindness I've picked up has filled into an empty slot in my toolbox instead of into a bag.
Just remember than only things under the Tools heading in the Encyclopedia count for toolboxes- machine parts do not meet that requirement, while things like Emo Bears, Random Kindnesses, and Quills do.