An lot of plastic can be recycled, and much of what cannot is being phased out.
I only shop in supermarkets that only use recyclable plastic for dairy products and meat which are the things commonly sold in plastic.
All plastic bottles here are recycable and many you pay a deposit on which is refunded when you hand the bottles in again.
I have said it before, but will say it again - the deposit system makes people more interested in not throwing plastic down any old where. Not, of course, in the interest of the environment, but because they get money back.
Some people don't bother, but then someone who is living on social security, or is homeless will come along and collect the empties, as they do need the small amount that is refunded.
If you are buying anything made of plastic, and let's be honest, we nearly all do occasionally, make sure it was made of recycled plastic.
And if it really does n ot pay to clean cardboard food containers so the cardboard can be re-used, it should be collected seperately, and burned in a commercial facility that channels the heat generated to the district heating plant - problem solved!