Those things only break down if they're constantly wet. I started using them a few years ago for my peppers and tomatoes. I had some problems this year using those with some hot peppers this year. The roots found their way out the hole in the bottom, but the ones that tried to grow through the pot itself took forever to do so, and were constricted by the sides. Weirdest rootballs I've ever seen. Some are made of compressed peat, and some of them are made of unbleached cardboard/paper, I've used both, but not for weed.
The peat ones are usually square and seem to break down a bit more easily.