It has a lot to do with the mechanism of coupling. Copper makes an excellent electrostatic shield, but it is useless at preventing magnetic coupling. Can you pick up a (US) penny with a magnet? Nope.
If mu-metal is too expensive, a couple of nested layers (separated by a gap) of steel shielding may do an acceptable job. But you'll end up with a package that's a lot bigger, for a given amount of effective attenuation, than if you'd used mu-metal.
High-quality input transformers use a combination of magnetic (e.g., mu-metal) and electrostatic (e.g., copper) shielding.