Recent arguments about the proper roles of government have mixed these together and clouded the issue. Let's take them one at a time.
The first service class includes items like national military support, public health and the operation of the government itself. It is possible to eliminate these common services. For example, there are many countries in the world where defense is handled on a regional or clan basis. Health services are provided by charities or private care institutions. It is generally believed that this is not a good model for modern industrialized states, however.
The second service class includes old age pensions, unemployment support and some health services. The government collects fees from the populace, puts it into an insurance fund and then pays it out when a service is required. The guiding principal is that the risk is spread over the covered populace and thus the cost per person is moderate. By having the government administer the insurance programs it is hoped that the costs will be kept low, since there is no profit to be paid to the insurance company owners. Furthermore since the government can't "go broke" the insurance funds are safer than those of a private fund and less susceptible to fraud or graft. In the US, at this time, we have a mixed model with some insurance provided by the government and some by private sources. In many other developed countries the government funds play a much bigger role and the insurance extends to other types of hazards.
The third service is provided by the legal mandate given to government. It is supposed to create and administer laws which are fair and equitable. Imagine any team sport without rules or referees. Experience has shown that neither the teams nor the fans find this acceptable. Without an independent referee disputes in a game could not be resolved. Most fans and teams are willing to put up with the occasional bad call rather than no calls at all. The same thing applies in government. Lately there has been a great deal of discussion about the power of the free market to regulate itself or the "invisible hand" to sort things out. Hundreds of years of experience has shown this not to work. Time and again markets have become unstable, either with bubbles such as the famous tulip mania or the "South Sea Island" bubble, or have become overly concentrated such as the standard oil trust. This leads inefficiency, since prices are distorted and resources are diverted from innovation and expansion of socially useful tasks. Without a referee the situation eventually fails anyway, but later and with more social damage than a well regulated society would provide.
So those arguments for "smaller" government are confused. Do they want less common services, or less insurance or less regulation? It seems there are some calling for each of these, but they get lumped under a common label thus making coherent discussion of the merits or demerits of their positions difficult. At the risk of get mired in a labels dispute I would call the first group "traditional conservatives". (Neoconservatives want larger common services in military and police areas). The second group are "Libertarians". They believe people should take responsibility for their own present and future well being and seem not to understand the laws of probability; or, that misfortune is not a "failing" of character. The last group are the "free marketeers" or "social Darwinists". They believe that regulation inhibits growth even though the opposite has been shown to be the case for hundreds of years.
Modern society is going to continue to have government perform all three
functions. These have developed because there was a need, and because they
worked more often than they failed. Progress will be made when the critics
stop trying to turn the clock back to an imaginary past and devote their
energies to optimizing what we have. "Liberals" can also do their part
by focusing the discussion on the roles listed above and proposing improvements
targeted to each sector.
Moral: Government is not the enemy