LCA's are only as good as the person who performs them. But we'd be much better off if everyone at least knew what they were, and what they try to accomplish, specifically capturing all of those externalities.
Re: the tax and ban... Tires and lead batteries in most states in the US is good example of this. You can tax or ban or regulate to put a cap on the problem. But if you want to collect the existing waste already out there, an incentive refund accomplishes much more, in less time.
Plastic bags in the ocean are an externality, whose cost is hard to measure but is paid in the lives of wild things. The whole point of externalities is that people aren't bearing any cost for them: tax and/or ban is absolutely a reasonable approach to handling them, since it makes people take literal account of the literal downstream effects.
One more thing, on edit: the analysis you're calling for is good to do, but is also prone to the "seeing like a state" problem. The analysis will only include what can be easily measured... Which can leave out a lot of the story.