[...] there is a kind of puritanical view that everything relating to nicotine is bad and harmful and should be stamped on.
I'm no expert on this topic, but it seems to me that the harms of tobacco are from smoking (and chewing) and not from the nicotine itself (apart from the addictiveness). So nicotine administered with gum/patch/vaping would be somewhat more like caffeine in harmfulness (loads of people are addicted to caffeine).
Nicotine also seems to have similar useful effects. From Wikipedia: "Nicotine appears to have significant performance enhancing effects, particularly in fine motor skills, attention, and memory." A Martian scientist comparing the harms and benefits (for humans) of drinking coffee vs vaping nicotine might think that both drugs are safe and have productivity-boosting effects, and wouldn't see a reason for only one of them to be socially acceptable.
So why is nicotine held to a much higher standard? Well, the public health effort to end smoking became a moral crusade. As Jonathan Haidt puts it, morality binds and blinds. The anti-smoking crusade gained enough strength that it created a hated enemy. Smokers in North America are now a low-status out-group from the perspective of most non-smokers. As usual, when activists morally charge their case by painting something as sacred or evil, they commit themselves to not giving up an inch. Smoking is pure evil, and nicotine is central to smoking, so nicotine must be evil too. Any admission that nicotine might not be horrible is helping the enemy.
Caffeine, on the other hand, did not get loaded with negative affect because it had a safe delivery system. Imagine if nicotine had historically been consumed in drink form instead of smoking -- in such a world, I imagine that it would just be another stimulant drink like coffee or tea.
It's a real shame that e-cigarettes (nicotine) are being morally condemned along with cigarettes (tobacco). If smokers can switch to vaping, they can avoid all the harm and still get their nicotine. From a public health perspective, getting smokers to switch is a huge win. Doctors should be prescribing e-cigs to smokers, government should promote switching. Unfortunately, since nicotine has been painted evil by association, it's probably not going to happen.