The important factor isn't whether someone can be addicted (otherwise you're banning nearly everything), it's the harm that addiction causes. As a general rule of thumb physical dependencies like alcohol are more harmful than habitual addictions, but that obviously isn't the whole story.
Caffeine addiction is the same category as alcohol and tobacco but causes so little harm that I don't think anyone is seriously opposed it. On the other end of that scale is something like meth or other hard drugs, generally understood as destructive and has few serious supporters encouraging use. Breaking these addictions is almost always hard and physically taxing, in some cases can even be lethal.
Marijuana addiction is in the same category as most things that make you feel good or form habits so it's harder to nail down a proper scale, but the lower end is probably something like video games; a debilitating addiction is possible but uncommon and most people would oppose a blanket ban on the basis of "can be addictive". Gambling is on the other end can definitely ruin lives. I'd say that's a little worse than coffee. Breaking these addictions is more like breaking a bad habit, it can feel hard for the addict but generally isn't going to kill them.
The British monarchy primarily "provides" money by owning land and other assets which would otherwise be government-owned. They also "earn" a shitload of money just for existing and still dump significant expenses onto taxpayers.