The interesting twist is that, the stronger is the evidence for rational addiction - in other words, the more closely the demand elasticities match for the two groups - the more likely it is that a tax increase will reduce addicts' consumption at a reasonable cost in terms of deadweight losses imposed on moderate consumers. However, if the rational addiction model really holds, then such taxes are not welfare improving absent the specification of a highly paternalistic social welfare function. So, alcohol taxes work to stop "harmful" consumers' drinking when those consumers don't really need the help.
On the flip side, if the rational addiction model fails to hold and the real story is a behavioural one about weakness of will and self-control, then "harmful consumers" might prefer that something be done to help them quit. However, in that case, we're outside of the rational addiction model and the price elasticity of demand will be near zero: in other words, taxation is no longer an effective mechanism for reducing their demand. In the state of the world where the rational addiction model does not hold, alcohol taxes will not make addicts better off even though those addicts would prefer that their consumption be reduced. Instead, the alcohol tax just imposes deadweight costs on moderate consumers.
Long story short: if alcohol taxes work to curb addicts' consumption, then we probably don't need them because that consumption is more likely to be rational. If addicts really are irrational and need help to curb their consumption, then alcohol taxes won't work to solve the problem.
On the latter point, a recent NBER working paper gives some evidence on short run demand elasticities across cohorts of drinkers. They use a finite mixture model to allow heterogeneity across latent groups. They then find that short run demand from heavier drinkers is indistinguishable from zero. They consequently argue:
[I]n the case of potentially harmful goods, sin taxes are levied in part to reduce the potential harms, external and internal, of consumption. For these drinkers, under several behavioral economic theories of addiction, taxes could increase welfare by serving as a precommitment device that serves to bolster weak self-control. However, our results suggest that the heavier drinkers are least likely to respond to the higher taxes, thus neither the externality nor 'internality’ justification for higher alcohol taxes is supported by our results.I'd like to know what their approach would say about longer run demand elasticities. I continue to hold the view that the rational addiction model explains a lot about the real world. I'm also happy to accept that demand elasticity among high demanders is lower than that among low demanders; consequently, I worry that excise tax increases, even if effective in curbing some "harmful consumption", induces disproportionately large deadweight costs on moderate consumers.