Basically, you "wear" a shield on your arm, but wearing it prevents you from using that hand for wielding a weapon or implement. The way the CB (and 4e in general) works is that you have your main hand and off hand available. If you have a shield, that "fills" one hand. So you can't wield a greatsword with a shield strapped to your arm. Neither can you wield a short sword or a wand in both hands with a shield strapped to your arm.
So, magic or no, a shield will prevent a hand from being used to wield a weapon.
On the other hand, a bracer doesn't prevent a shield from being strapped over it. Instead two "overlapping" magical effects will interfere with each other.
For magic items, there are a number of slots. Arm, hand (gloves), fingers (rings), held objects (weapons/implements), etc. You can hold two different items, you can have a single ring on each hand, one "pair" of hand items, and a "pair" of arm items. While a shield counts as an off handed item when "wielded" as getting the benefit of it prevents you from using that hand to wield another held item. However, they felt the need to prevent using magic shields as an "extra" slot. So, if you have a magic shield, it counts against a magic slot (held item is 'technically' a slot, but in some cases, like a two handed weapon, you are using both hands on the same item) and arm makes the most sense.
My "any armor" comment is basically this:
There are some arm slot items that anyone can use, whether they have no shield, a light shield or a heavy shield. These are basically the bracer types. Other effects only go onto shields (and some only onto some types of shields). These magical effects are more specialized because certain builds (like people that wield two handed weapons or aren't proficient in shield use, etc) can't use.