Don't cut off someone's head if they have a headache, maybe try giving them less booze.
A state imposed pigouvian tax sounds wonderful until one studies the cause of the initial externalities. Frank's example of a Soda tax is a perfect example for this criticism: If high fructose corn syrup is a societal problem rather than taxing it why don't we just stop subsidizing it? Franks argument would hold up better if he didn't use such terrible examples.
I like the core concept of a Pigouvian Tax. A fee on a negative externality, simple and reasonable. Pollution, waste, is a sign of inefficiency. In the market the goal of a firm can be profitability; if a firm is wasting money on fuel for inefficient capital then their profit margins are lower. This is a structural mechanism of the market, an implicit fee on an externality, not because pollution is morally wrong but because it is wasteful and expensive in the long run. When property holders are sensitive to long term costs than efficient production is incentivized. But a state pig tax is not a market mechanism, it is an arbitration enacted by someone holding a gun.
The imposition of a pig tax is not only difficult, it is dangerous. The more basic a negative behavior the easier the tax method. If the goal is to tax sugar where should the tax be imposed? On the producers? Or perhaps those who use the product? Try and figure out a way to impose to taxes on a edible good, the difficulty is surprising. Aside from the obvious imposition issue there is of course the communication issue, the likelihood of taxing a subsidized good is quite high. There is also the danger of setting the price too high and hurting what could have been a competitive firm.
How can the pig tax be used in a positive manner? Let firms use it in the form of a fee. If a firm is actually sensitive to costs and externalities it can use a pigouvian structure within its own confines as a means of resource allocation. Crowdsource the model! Many people impose fees upon themselves to limit their own behavior, why can't firms? A spontaneous group has great opportunity for innovation if the service is not already monopolized by the state. Violence is not the only solution to curbing negative behavior.