Why do laptops' chargers have coaxial cords?
The plug is coaxial because it can't be easily shorted when pressed in any orientation against a metal surface, and there's no orientation issue when inserting it into the laptop.

The cables are rarely coaxial, but when they are it's often more for the aesthetics of a very thin round cable than it is for anything electrical.  You can make non-coaxial cables that have round outer profiles, but they are thicker, as the cable has to have a diameter at least twice the diameter of the two wires inside the cable.

If you're carrying three wires, as with grounded outlets, the diameter of the cable isn't going to be much less if it's coaxial, so there's little benefit to making it coaxial.

However, if you have only two wires to carry of a specified gauge, then you can have a thinner, round cable profile if it's coaxial.  

It does increase safety, slightly.  If the grounded conductor is the outer conductor, then any cutting or piercing of the cable will result in a ground contact first, before hitting the (typically) low voltage core wire. These supplies are isolated anyway, so it typically won't matter, but it does mean that if your cable insulation is damaged and that comes into contact with a metal part of the laptop, you won't see sparks, kill your laptop, or the power supply.

EMI concerns should be negligible on this cable, but it may help with them in some small degree. Typically you put filtering on the laptop and the power supply so nothing but the intended signal goes out on the wire, and nothing received on the wire goes into either device.