An attempt was made some years back in my country to ban plastic bags. It is indeed a major problem in my country with millions of users of these bags, many of them being uneducated people. The streets in every city in my country are littered all around with these bags. Then when the rains come, these bags choke the drainage system of the city leading to streets getting flooded.
The campaign to stop the use of these bags was a total flop. It led to clashes between the consumers and the authorities. There were two major reasons behind the failure of this ban. First is the cost of these bags. They come in very cheap. Shopkeepers never refuse to give you an extra piece free of cost should you ask for one. Secondly, they are very convenient to both the sellers and the buyers of items.
Having said that, I cannot see them ever getting banned in my country, and possibly also in the countries in my region. It is one of those things that progress in science and technology has given us which has become part and parcel of our life. The only alternative I see is to find a solution for their proper disposal in a cheap way. I do not know if they could be recycled but if that was possible, we should work towards achieving that goal.