My neice uses this method for her veg plot .I've not heard her say anything against the chemical .but her veg results are very good.
We aren't allowed to use carpet on the allotments because of the chemical and the fact that it is proper minging when it's wet.
I'm using "lasagne" gardening on some of my beds- newspaper, water and straw. That seems to be working very well indeed. I'll just compost the straw and dig in the newspaper. We also have a large piece of poly covering one bed and it's not as good as the newspaper method
I thought that woollen carpets with woven backs were OK, but foam backed ones are a definite "no no".