As far as seat belt laws, there has been a fair amount of opposition to that. I remember a lot of people didn't like it and resisted those laws when they first started being introduced. I remember hearing that among the biggest advocates for seat belt laws were automobile manufacturers. I don't know if that qualifies as a "nanny state," although I can see where some people are coming from on this issue.
However, the term "nanny state" carries the implication that the leadership in our society actually cares, which I might sometimes question. Sometimes, it looks to me like they just want people to think they care. It seems more a matter of political expediency than anything else.
The nanny state has also taken different forms, I suppose. The enactment of Prohibition might be an earlier example, but that turned out to be a disaster, much as it has turned out for the modern nanny state which is obsessed with a war on drugs. There were people who wanted to ban jazz because they thought it was the "devil's music." Now that's some real "nanny state" right there - or at least an advocacy for one.
On the other hand, drug abuse and alcoholism are serious problems in this society - problems which are severely pronounced among the poor and lower classes. But the current practices of the War on Drugs (which has its initial origins in earlier eras of systemic racism) are simply not working. Nanny just doesn't seem to know what she is doing much of the time, so the idea of "ban this," "limit that," and impose more and more rules upon the common people doesn't go over very well. Even if it's paved with good intentions, and even if Nanny really does care, deep down inside - we might consider alternative methods of achieving the same goal.
Another thing to consider is that, in practice, it will turn out to be another excuse for police officers to harass Black people. What if menthol cigarettes are banned, and a Black person is standing on the street smoking illegal menthol cigarettes? The police would be duty-bound to approach them, arrest them, and confiscate their cigarettes. Another unnecessary encounter which would have the potential for turning deadly. There would be many encounters like this of the kind of we've seen in the past when police go after people on piddly violations - and this would be just another to add to the list. There would be a new underground market for menthol cigarettes, which could lead to other kinds of problems.