I used cardboard before and it only lasts one summer generally. I did use some shingles for a pathway once and there were some issues. They were down for 6-8 yrs if I remember right. But when we moved I wanted to take it out and restore it to lawn. VERY difficult. They had become brittle and broke off tiny pieces at a time and were hard to get up out of the soil (which was actually clay underneath). Would be ok if you wanted it long term and had the understanding going in that taking it out one day might be a chore.
Even if carpet did not last forever (and what does?) it would still last 4 or 5 years I would think and that would be better than most materials. If you kept it mulched (protected from the sun) it should last decent I would think.
