Our council does it different: we pay £1.50 each for the garden waste bags, but the collection is free until the bag falls to bits and you have to buy a new one.
Burial/cremation is an issue too so I don't think that works either @Lyn😕
It's a puzzle that not all councils operate the same system for collecting waste, but I think it makes sense when some charge for garden waste collection if the area is urban with a majority of properties with no garden. Those who say they don't pay for collection are in fact already paying for it via their council tax, and people who live in homes with no garden don't need that service.
The system here works as follows:
recyclable waste - including food - every week.
non-recyclable waste twice monthly.
garden waste twice monthly.