Runs where? You say you live in Canada, how is your health care system financed?
Interesting. What kind of laws would you suggest to deal with these two of Pigou's own examples of proper use of that kind of taxation?
The purpose of Pigovian taxes is to convert an externality to an internality. By putting a tax on industrial pollution, the government "encourages" the factory to build a wastewater treatment plant instead of just dumping their crap on someone else. If the tax is high enough, building that treatment plant becomes economically favorable, and the customers end up paying what the product really costs instead of dumping some of that cost on someone else.
Our health care system is financed, as you know, through taxation. I wish that it were not. I would much prefer people being left alone to live as they wish, and purchase the health care that they want. Instead, products like alcohol and tobacco are surtaxed and the revenues are supposed to be funnelled into the public health care system to compensate for the damage. I think that this procedure is in line with the external/internal idea. I believe that the higher prices that the taxes create are also intended to dissuade usage. My view is the opposite, in that people should manage themselves, and do their own personal internalizing/externalizing, when there are actual consequences for their actions. I am against the government being so involved in peoples' lives. If someone smokes, and their insurance premiums are substantially higher on the free market, or they forego insuring themselves, the risk that their medical costs due to smoking-related illness could be substantial or even bankrupting may make them consider not smoking voluntarily, or through necessity. The money that individuals would save on taxes would be in their own hands for their own use in purchasing what the government now does for everyone, without consent. For the criminal element referenced with alcohol, if the government was less involved is spending peoples' money on their own healthcare they would have more to put into law enforcement.
If the industrial polluter, or misplaced development project existed in my world of less taxes and more laws, both would be simply denied the ability to do what they do. If the industry cannot manage their pollution themselves, and not pollute acccording to the laws, then they would be shut down. They can move to China. For the developer whose project would negatively impact the local community, if they break laws intended to preserve a quality of life for resident citizens, they would be shut down, or construction permits denied. There are already plenty of laws in these regards. I do not see how taxation figures into it.
Similarly, with respect to taxes, petroleum products are also subject to high government surtaxes, and following the internal/external idea, those additional tax revenues would ideally be used for smog reduction or roadway maintentance projects. Subsidies are also funnelled to public transport services, making them more affordable, and hopefully persuading people to leave their cars at home, and engage in the win-win scenario of cheaper transportation with reduced impact on the environment. There is some merit to be seen here, particularly if you have visited Mexico City or Sao Paolo. I believe that infrastucture does fall within the mandate of a government, so with respect to roadways, am not opposed to taxation of vehicles, fuel, or both, as long as the money goes directly into those areas. What we do not see however is more choice for the consumer. There are no tax credits for the purchase of electric vehicles. This, to me, punishes both the automotive industry and the consumer. Where I live, gas prices and taxes are among the highest on the planet, roads and bridges are crumbling, highways are jammed all the time, hospital waiting rooms are overflowing, patients sleep on stretchers in the hallways, boarded up buildings and storefronts abound, personal and state debt are out of control, but the government is still hiring.
There is clearly something wrong.
I do not have faith in government to resolve any of it.