I know that the after-usage environmental cost is completely intolerable, however making those cheap flimsy bags on an industrial scale involves refining less than half a gram of polyethylene, then stretching and cutting it , so the unit carbon cost is relatively low. >
Paper bags have a high unit carbon cost, partly offset by the embodied wood pulp,but increased by the heat and water needed to pulp and roll all that paper. They are much less impactful if they do reach the natural environment, however ,which is why they're preferable.