Although technically true, if you apply a reasonable discount rate the analysis flips back in favor of smoking cessation [1].
If you ignore the fact that old people aren't just sent out the pasture to die, then sure, maybe you can set gamma to an unreasonable small value, you can decide that more early death is cost-effective.
But such an analysis, which again nets out positive for smoking cessation when applying an appropriate discount factor, ignores the fact that healthy older folks still contribute to society.
The retired population is an enormous social asset. They contribute disproportionately to community volunteer work, play an important role in family formation/childcare, and many also work well past retirement age. The average retired person is still performing an significant amount of socially valuable labor, regardless of whether they're filing a W-2. In many communities/families, Social Security and Medicare are at least in part a significant state-subsidized childcare allowance.
[1] https://www.nejm.org/doi/full/10.1056/nejm199710093371506
You need to apply a discount rate of 10% (which seems unreasonable for the government which can borrow at incredibly low rates.)
Also this analysis ignores that healthcare costs are accelerating faster than inflation, so treatment for an individual in 20 years will likely be far more expensive than treatment today.
It also doesn't include social security.
I always thought a solution would be to tax beers 1 dollar, and then give it back to the patron in untransferrable rideshare credits.
The data on drinking is much fuzzier (because so many people drink in moderation) but my impression is that, as you suggest, it's significantly under-taxed relative to its negative externalities.
Edited to add: For comparison, IIRC a Pigouvian tax on sugary drinks should be something like $3 per 12 oz can. People who drink lots of sugary beverages also tend to die sooner, but they use a ton of medical resources while they're around - the average lifetime treatment cost of Type 2 diabetes is over $100k, and that's just one condition.