Those shag carpets disintegrate very fast, and it doesn't matter which side is up.
The carpets with very little nap last long enough, but carpet is made from some toxic stuff...
Having said how awful carpet is... I still use it...
Down here in middle ga, there are some perennials that can not be gotten rid of.
Things like stachys floridiana, Saponaria officinalis, Cyperus rotundus, Cynodon dactylon...
Unkillable...
A sheet of plastic, topped with an old carpet, covered with a thick layer of wood chips... left in place for a number of years... seems to help...
And...
A carpet right side up might be suitable for helping something to grow on a packed clay slope... where nothing can get established any other way.