No, "distributing risk over a broad base" is not the reason that government should provide police, fire protection, and national defense. The government provides police protection and national defense in order to defend our liberty from the aggression of other people. Socialized healthcare doesn't protect us from aggression; rather, it tries to protect us from our own poor planning and bad luck. If you think that's the government's job, then you will also want to socialize a lot of other things -- retirement savings, education, housing, nutrition, childcare, employment, etc. That's socialism, and if you believe in it, you should just say so.
Fire protection is an interesting case. Fire protection only needs to be socialized where free-riding would cause catastrophic undersubscription to it -- basically, in places where fire can easily spread from one property to adjacent properties. I can free-ride on how your private fire service will put out my fire to keep it from spreading to your property, but there's no danger of me free-riding on your private healthcare. You can make a free-rider argument for government protection against fire and flood, but the argument doesn't work for healthcare or education or retirement savings or all the other things that leftists want to socialize.
Possible follow-up question: But can't you free-ride on my charitable donations toward a healthcare safety net for the poor?
Answer: Yes -- just as I can free-ride on how you broadcast TV and radio programming, how you donate to the arts, how you landscape your yard, and how you pass on funny jokes. Would all these things be catastrophically under-provided if government didn't forcibly extract money from us to finance them? Surely our society would be wealthy enough and charitable enough to provide an adequate safety net, if the government got out of the forced-charity business and got out of the way of healthcare competition and innovation. Note that over the last century or more, waiting for one generation of economic progress has helped the poor as much as, or more than, even the most utopian proposals for income redistribution.
Geolibertarian follow-up answer: And if you agree with me that land is a special kind of property, and that planting a fence or a sign in the ground is not the same as producing something with your own labor, and that each person has an equal right of access to the Earth's atmosphere and surface area and wind and rain and sunshine -- then you will agree that a natural safety net should already exist. You will agree that the medieval notion of absolute royal "title" to some part of the Earth's surface is unjust, and that people excluded from land have a right to share in the extra return that the excluders reap merely by enforcing antique property boundaries. In principle, that extra return is the excess production obtained by using a site in its most productive use, compared to the production obtained by applying equivalent inputs of labor and capital at the most productive site where the application doesn't require new payments for use of the site. In practice, this right of equal access could be enforced through a citizens' dividend financed by a single tax on land value -- an idea widely defended by economists as the most fair and efficient tax system.