What I mean is that when you press A on an item in the centre or right item bar that already exists in the left item bar, it should delete it from the left side, rather than doing nothing.

This is generally an antifeature, you can easily remove favorites from your favorites bar with the keybind there, having favoriting function as a toggle in the index and other places is confusing at best and could remove items players care about at worst.

No, no—if my favorites list gets too cluttered, it becomes really hard to find the item I want to unfavorite... If that's not convincing enough, could you at least change it from "no response" to "move to the bottom"? You could even add a config option for this feature.