I spoke to a bin man about this and he said that his colleagues are completely opposed to the system, which already operates in some areas they cover.
They find the bags difficult to lift and carry, repetitively and because they don’t hold as much cardboard as the bins, people leave excess stuff alongside the bags, meaning they also have to pick up piles of sodden (at least I THINK he said sodden...) cardboard on their rounds.
My pet peeve is the council literature saying how marvellous it is that the bag (holding paper and cardboard) has a larger capacity than the caddy (holding only paper and usually full). As someone who has spent many years employed to present a positive perspective on sometimes unpalatable news, I hope I’ve avoided anything that transparently insulting to the intelligence of readers.