You can't ban stuff because bans would be full of loopholes for "necessary" usage.
You can't just appeal to people's better nature because humans are humans.
You must live in the alternate universe where everyone litters.
No, some people just don't litter. Whole cities where people don't litter! Sometimes, there is a clear protagonist and antagonist.
As an aside: an* effective means of keeping that cup out of the ocean is also to buy all the cups and not use them. Pretty much the exact OPPOSITE of a "pigouvian tax." Isn't that crazy?
What if we bought all the oil and didn't burn it? What if we buy all the land it's under? Or more realistically, what if I bought carbon credits in cap and trade and didn't use them?
Greg Mankiw has doomed a generation to inside-the-box policy with his inane textbook.
In Seattle we've banned the cheap plastic bags that blow around and get stuck in trees. There are many, many fewer tree-stuck-plastic-bag-ghosts to be seen around now. We've also put a mandatory 5c fee (not a tax, sadly) on paper bags; there are many, many more people bringing reusable bags to the supermarket.
(Ignores, of course, whether these reusable bags are better for the environment holistically -- having lots of yuppies buying synthetic shopping bags made in China and shipped to Amazon DCs, then having them individually shipped out in Prime boxes, etc. before being used is probably worse than just having pulp grown in America made into bags trucked en masse to the grocery and generally recycled or composted.)
Regarding carbon credits -- soon that will be not only feasible but tokenized and sub-divisible. See http://sparkchange.io/
eg if k-cups cost 2c to produce in plastic, and tax raises that cost to 5c, and margins were at 4c so now 1c, then it makes sense to start looking at alternative materials/strategies that weren't previously cost-effective.
At the same time, auto using a good deal of plastic per car, but much higher margins, and much less plastic use across the total market, might have their costs raised by $200 in total per car by the same tax; but if they had a $5k margin now dropped to $4.8k, they probably don't need to change much (they're still affected, but not nearly as bad).
The problem with plastic is that its cheap, so it can easily fit in disposable markets, but we really don't want it there, and disposable markets tend to have razor-thin margins. Ofc the strategy I just described might not actually affect K-cups: K-cups are really the only thing I can think of where plastic got added to make it a luxury product, rather than removed (cars otoh are luxury despite the plastic). And being a luxury product, it's probably got decent margins and can eat small tax increases.
But you can probably get 90% of the way there with minor taxes. And ofc you'll still have necessary usage for certain things (lets say, emergency shelters), but you can avoid adding loopholes to plastic by lowering less tax-burdens on other aspects of the target industry, which might be less viable/harmful to abuse.