Plastic is fine. It has it's uses, and we won't get rid of it anytime soon. We need to get rid of the bulk of the one-time use stuff though, and focus on re-usable items if we want to change something.
I do want to add though that if we had greener transport, then heavier items wouldn't be that big of a deal. So if we are playing the long game, that would almost be a good incentive for transport and industry to be more efficient in the long run.
It has historically been plastic because it is cheap and readily altered to match the exact needs of the product. Rigid, soft, rugged, smooth, coarse, we can make a plastic suit.
Plastic cups are a good example, we have numerous materials at our disposal but we make disposable cups and containers out of plastic. Even bio-degradable plastic cups are a bad choice of material, as they take special circumstances to break down that many municipalities don't provide for and most users aren't carrying their bio degradable cups home to put in their compost. If they end up in the ocean, they will last just as long as other plastics. So that is bad product design, it doesn't take the full product lifecycle into account and ignores even it's typical usage of just a single serve drink used once.
Plastics have spoiled us too, so in many cases there probably isn't an alternative that is just as good. We may just have to accept that and find ways to make better materials out of more sustainable sources.
But, I missed it if you said it - what material should we ideally use for disposable cups, currently?