I suspect that making metal insulated cups is cheap these days. Perhaps this could solve that. I doubt people would hoard mountains of them. Then it becomes a matter of paying for the hoarded ones. People hoarded and still do some glass bottles where glass bottle replacement schemes exist/have existed.
Thinking more on this point, a genuine replacement for single use plastics for beverages could be a soda can equivalent, cheap, double wall aluminum container. If someone can make such a container for low enough cost, that could be a solution since aluminum is infinitely recyclable.