We have compostable bin pickup twice a week in my hometown in Italy, a ton of things are compostable with industrial composters these days which you could not easily compost at home, also thanks to regulations (e.g. shopping bags, tea bags, some food packaging etc), so the other bins stay pretty empty.
Important to note that, at least in my experience, most of the 'plastic bags' in Italy are the compostable kind. In the UK they're still in the minotrity (I've only seen our version of the Co-Op offer them, for instance).
You might wish to be wary about tea bags, mind - here in the UK our tea producers are still struggling to release bags free of thin heat-pressed polypropylene sealing strips... .
