I seen that done before, it turns into a big mess when it starts to decompose in >3 years... It will break a lawnmower and tangle into weedeaters.
Black weed suppressing cloth last about 10 years and looks a lot nicer.
Also weeds love to grow on the moist surface of carpets. So you would have to spray the carpet with roundup to stop weeds from sprouting on it. Which defeats the purpose.