"There is something to be said for protecting the public health though, don't you think?"-Thucydides
Not sure who that's addressed to, but no.
Firstly, stop calling this damned thing a tax. It isn't, its a fine for going against an unwritten law. It exists not to raise revenue, but to punish a certain behaviour. Raising revenue would be a side effect. The same applies for "green taxes", alcohol duties etc.
Secondly, the evidence of alcohol, green taxes, tobacco etc. is that it doesn't significantly reduce consumption.
Thirdly, it is restricting my liberty. It is arbitrarily reducing my capability to make a particular choice. It is equivalent to putting a toll on walking down certain pavements and claiming that I'm not restricted from walking down them. An outright ban and a tax is a matter of scale. A tax of 100% (to double, as you suggest Thuc) may restrict me (actually, more likely, I choose not to buy some other goods). A tax of 100,000% stops me completely. If this policy is to work, then it does so through compulsion, and is as good, or rather bad, as a ban.
Fourthly, it is not the role of government to protect people from themselves. It is the role of government to protect people from direct attack from others. You should have "life, liberty and the pursuit of happiness" delivered by government, not "health, education and a livelihood". The difference is that government should be protecting the means of success, not providing the end goal. Aiming to achieve that end is the thing that gives meaning to being human.