If humans are to stay on this planet, in the long term we cannot just keep piling up garbage in landfills and building on top of it. Eventually, in hundreds or thousands of years we will have to remediate that land. Its going to be a lot better if we just make our waste as recyclable as possible in the first place.
The author is recommending a half measure based on the assumption that the US cannot fix its own problems. They are also implying a false equivalency: banning single use plastics is not the same as recycling plastic. A more equivalent comparison might be the tradeoffs between plastic bottles for soda, water, or oils and glass or metal containers. It is also true that plastic straws are a much smaller problem then other usages of plastic such as bottles or event fishing gear and even bags.
Yet there is nothing inherently wrong with reducing plastic usage. Doing so is smart and will be important for the health and well being of future generations -- human and nonhuman -- of life on earth.