When I assign my inventory to 'Tab', I am able to open my inventory, but pressing the key again to close it doesn't work. Instead, it tries to select something, in survival the crafting book and in creative it doesn't find anyting.
This problem isn't exclusive to the inventory, but any type of crafting or container UI. Using escape closes the UI like it normally does.
I beloeve that this has been a bug ever since the accessibility functionality of the 'Tab' key was introduced.