Last thing first, if the cable is properly lubricated, all the pedal/cable is working against is the return spring on the carburettor cable linkage, and the tension to do that will take some time (years) to wear through the (original hard nylon) grommet. Furthermore, the grommet holds the cable centrally in the tube to stop it dragging on the inner wall.
In my experience, there are two main causes of cable problems on the a/c (I don't know if the Bis is similar as the carb position is different) and they are "the tubes".
The first is the one on the driver's floor on RHD cars which links the throttle pedal across the floor to the cable lever/nipple inside the central tunnel. The second is the tube from the central tunnel through the rear bulkhead into the engine bay. I can't recall if this second one carries the throttle cable or not, but from what you say it does.
Both of these tubes are simply mild steel, and as you can imagine, at manufacture Fiat realised that to avoid corrosion they would have to be galvanised, Ziebarted, Waxoyled and generally anti-corrosion treated to the very highest standards.....
But as that would cost way too much they just thought, sod it, let someone else sort out the problem... and guess who that 'someone' is? Well a year or so ago it was me, but today it's you!

The only way I can see to really get to the bottom of this issue is to remove the cable(s) from the tube, then ream it out to remove all rust, dust, grot, dead grampy grunts, spiders' nests etc, and douse it liberally with waxoyl. When you re-insert the cables, make sure they are equally doused in oil/WD40/bitumen/tar etc so as to prevent future corrosion.
The Fiats are lovely little cars, but sometimes I look at some details of the design, and I do wonder what they were smoking at the time...
I suppose in Italy where it never rains this isn't an issue. But in the Northern Isles...

You might try something like this:
http://www.ebay.co.uk/itm/White-Cleaning-Brush-Glass-Laboratory-Lab-Tubes-Instruments-Tubing-/191743850686to clean out the tube. Thread a stiff wire through the tube, hook it to the brush and pull it through completely so that the debris is pulled completely out. Or add wire to both ends and you can push/pull back and forth to give the tube innards a really good scrub!