All cars have them. The rear ones are usually carpet, and front ones are plastic.
I think they use carpet to reduce the noise from stones that are hitting the arch lining, that would be very noticable inside the cabin... Front ones dont need that, but I've seen some Audis with both front and rear carpet linings.
I agree that they're for noise reduction, and my guess on what decided whether the fronts get them as well, is that it depends on whether the front arch intrudes on the passenger cell at all.
In the long nosed 156, it doesn't, and they have none. I've been told by 147 owners, which is short nosed, and in which part of the wheel arch does intrude on the passenger cell, that they have carpeting at the front too.
Although Tribesman has a 147 and implies his doesn't.
Maybe only the 'luxury' 147 GTA then?
There is little to none difference when comparing 147 and 156 in regard to wheel protrusion inside the cabin. Both are designed on the same chassis. I have never seen 147, 156 or GT with carpet front arch linings...