Aren't carbon taxes like 'sin' taxes?

No. Targets of so-called 'sin' taxes such as alcohol and tobacco are end-use products, whereas energy sources are intermediate products that can be displaced by alternatives. That is, if you want to drink wine, your only option (other than making it yourself) is to purchase it, whatever the cost. But if you want to heat your home, you want to do so with the lowest cost energy source, regardless of what kind of source it is.