I think a big part of the difference is that most people get addicted to cigarettes just by being around it, rather than seeking it out. Cigarettes don’t get you high/drunk (well OK, you get a small buzz early on, but nothing like weed or alcohol).
People will seek out weed even when it’s illegal because the risk is worth the reward (to them), because it comes with an intense high you can’t really get anywhere else. I don’t see nearly as many people seeking out cigarettes in the same way, unless they’re already hooked.
I don’t think it will “solve” the cigarette problem, but I do think that prohibition for cigarettes won’t go quite the same route as prohibition for weed and alcohol.
Now, whether I want the government to be able to ban recreational substances just because they think it’s bad (or use that as an excuse) is another question