This is a great idea--I first used a similar-ish (if that is a word) product when living in Japan.  There, trash is sorted most particularly, and dog poo was to go in 'burnable' trash.  Rather than using grocery type bags there was a nice product with a burnable plastic and paper lining.  Very nice, but a little small.  Even with that drawback I found myself missing those bags and once again resorting to grocery bags once we moved.  Not good for the environment, and just not good in terms of quality.