I think that little piece of plastic doesnt really make a huge impact, its not a lot of plastic and we have so many other places where we could guide manufacturers to include less plastic in packaging.
Its much more energy intensive to produce a disposable vape, they contain more plastic, the battery has to be produced and its unlikely they end up in electronics recycling, where they belong.
Here in Germany some McDonalds and Burger King do have self serve drink machines with unlimited drinks, but they are not that many (I would guess 10-20%). Some other fast food chains are more likely to have them, like Subway.