Public cleaning should address difficult situations that need special equipment, like removing a lot of leaves and dust after a storm, to avoid obstruction of manholes. Or empty the public litter bins.
Until years ago, it was absolutely normal for my grandfather to cut the grass on the side of the public road in front of the house. Or for farmers to keep the ditches near the fields clean, to allow good irrigation when needed.
They were grateful for what they had and gave some help back.
If everyone does this, we have an orderly and efficient environment.
But nobody does that today.
The problem is not the 'government', it is the lazy people, the same people who ultimately build the government itself. And we are all a bit lazy, so I think improving our personal attitude is the best action to help us as a community.