Littering is the problem solved by charging for or banning free carrier bags, not usage of plastic bags. If your rubbish goes to landfill, don't expect a reduction in rubbish bags as a component. They're very light though.

IMO it's better to incinerate them. That's what Switzerland does. I think it largely works, as long as you have enough routes to take dangerous chemicals (electronics and batteries mostly, heavy metals) out of the the waste pipeline.