[Baertram]

Advanced Filters does this already.
But: The inventory cannot be split into exactly these crafting types as it comes prefiltered with standard categories (weapons, armor are strictly divided e.g. and cannot be combined on 1 filter to show "Smithing"). Same for Shields and staffs which are armor and weapons -> Not possible to combine them.
AF is providing subfilters for the given top category filters + plugins in the dropdown boxes which help you to filter them even more.
But that's all you will get as an addon ecept someone is totally rewriting the inventory...

A helper could be that AF is filtering the crafting inventories at the crafting stations as well,
and in addition FCO CraftFilter provides ways to switch between "Show bank", "Show only inventory", "Show both", "Only show craftbag" (at refine panel).

Another addon to help would be Inventory Insight as it also provides similar filters but shows ALL your toons/characters + bank + guild bank inventories in one UI.