Visible Armor Slots makes it so you can always have access to your armor from any pop-up menu. This may seem like a non-issue until you actually start needing to access your armor and don’t want to remove it, place it in your inventory, and then go back to the menu you were at previously. This is especially useful in putting your armor on as soon as you create it. Just craft the pieces and place them right in the slot.
But it comes in handy even more when you factor in enchanting and repairing since the slots are visible there as well!