An inventor in Japan is betting that you will. Akinori Ito has made the world's first home plastic recycling contraption. It takes commercial plastics, like bags and bottles, and burns them to generate oil. More work is needed to turn the oil into gasoline for a car, but it can be burned in heating systems or on stoves.
There are a few versions of the device. One is called the Desk-top Waste Plastic Oiling System, and is a relatively small version of recycler. A quick look at pictures shows that it does fit on a desk-top, but it would need to be a sturdy desk. The Waste Plastic Oiling System weighs a little over a hundred pounds, and takes approximately a two pound load.
The good news is, it is fairly efficient. The plastic is burned, and the fumes are corralled through a set of pipes and condensed back down to oil. Eighty percent of the plastic becomes oil. A two pound load gives around a quart. The energy required to run the system is a modest kilowatt for each of the three hours of running time.
The bad news is, it's still burning the plastic and releasing carbon dioxide. Bringing cloth bags to the store and reducing plastic, as well as reducing the need for gasoline and oil, is still a better choice for the environment. There's no such thing as a free lunch, even if the lunch costs $10,000.