Dog faeces in a plastic bag placed in a rubbish bin will go to landfill where the shit will ferment anaerobically (in the absence of air) and produce the strong greenhouse gas methane, some of which will then get into the atmosphere and make climate change worse – and the organic matter will be lost to the biosphere.
Dog, or any other faecal matter, that is left on the surface or buried (without being sealed in a plastic bag) will be decomposed aerobically by bacteria with the release of the less harmful carbon dioxide – and the organic matter will be returned to the biosphere.
I'm not advocating leaving your dog's shit for someone to step on, but I am advocating disposing of it with more thought.
In many parks or similar public places it will be easy to bury the poop beneath leaf litter or mulch off any walking path.
There invertebrates and/or bacteria will break down the poop and convert the organic matter into humus – that is, plant food.
I suggest picking up the droppings with a piece of paper (such as newspaper), digging a shallow hole in soil, mulch, leaf litter, or similar, and depositing the droppings there.
If you can kick the poop into the hole, or push it with a stick, rather than wrapping it in newspaper so much the better, because paper will take a lot longer to decompose than will faeces.