In my home province, Ontario, it’s now illegal to smoke in a car with a child in it [story]. Another sign of a growing nanny state?
No. A nanny state passes laws to protect people from themselves — “wear a helmet”, “don’t eat trans-fats”, “don’t smoke pot”.
A government passes laws to protect its citizens from each-other — “don’t steal”, “don’t drive drunk”, “don’t attack people with a hockey stick”, or even “don’t do noisy construction work at 3:00 am in a residential area”.
If you’re a hockey player, I support your right to swing your stick, but that right does not extend all the way to my face. If you’re a smoker, I support your right to smoke (tobacco or otherwise), but that right does not extend all the way to my lungs, or to your child’s. There’s nothing nannyish about that.
Quoderat 
A state that also provides healthcare has an incentive to pass nanny-state laws in order to protect itself from costs imposed on it by its citizens, as all three of your examples illustrate, albeit in decreasing order of aptness.
This is not a criticism of single-payer health care; I only wish I had it.
You are right, John — perhaps we all need a nanny sometimes.