If plastic bags are not curbside recyclable then throwing them in the bin doesn't help. Consumers absolutely do bear responsibility for the environmental impact of their consumption choices.
[1] http://www.bafu.admin.ch/umwelt/indikatoren/08484/08653/inde...
Only combustible waste is burned. Landfills are still needed.
Seriously, burning stuff is not good. We need to stop doing that.
For public trash cans: It happens that private security hides around the cans to control. I was once fined about 40 USD for putting paper in the paper bin on sunday at noon. They hid around the corner.