The reason it costs more is because workers still have to seperate plastics from other types of plastic. Also the garbage truck every week, which is also the reason for more pollution.
Plus all in all, the seperating plastics makes people moraly satisfied ( "they did their part, now back to buying more shit" ).
This city also has 3 systems which require at least 2 different truck types just for mixed garbage. (bags, underground container and bins)
Then there is the greens bin and the trucks for that. The paper bin and the trucks for those. And the plastics are picked up as bags or from a big collection container, so I guess thats 2 different trucks as well.
note: also there are big collection containers for paper and glass, which have different trucks as well.
We don't really need this little ritual of recycling to cleanse us of our consumerism sins. If we are really trying to help the environment, reduce, repair, and reuse is much more effective. Buy high quality stuff that lasts a long time.
Edit: Another bonus is that you and your neighbors only have to be woken up early once a week by the one garbage truck that comes by instead of three times with the current separate garbage, recycling, green waste trucks.