every character that as shield proficiency but will mostly be using bows as a free +2 AC permanently because it is free to switch what you are wielding in your hands.
Im sorry to break it to you, but this is even worse ... (i just checked)
Actualy every character that have shield proficiency and have Shield equipped simply HAVE +2AC permanently ... since the game is counting your shield even if you are wielding Bow ... so, basicaly, you dont even need to switch back to meele weapons (but you loose AOO if you will hold your Bow).
In some way it makes sense tho, AC is just number showing how much armor your character have ... and if you put your shield on your back, instead holding it in front of you ... the "amount of armor" surrounding your body remain unchanged.
You just switched better protection for your back over better protection for your front ... wich is something DnD dont concider at all.
