…the welfare state as social insurance.  

After all, if you know how your kids are going to turn out, what’s there to insure against?  Sure, you’d like to grab resources from other people–the raiding party has a long history–but it’s only when you’re not sure how your kids will turn out that you start fretting over whether insurance markets face major market failures and whether government-mandated redistribution can fix those market failures.  
Further, if insurance companies can tell a person’s productivity potential just by looking at the parental units, then it’s easy to write a private insurance policy that pays the person what they are worth.  If high (or low) productivity persists across generations there’s a weaker argument for insurance market failure. 
These twin facts–that when parental income is a better predictor of a child’s income, both:
demand for genuine insurance against life risk will be lower, and 
market supply of such insurance will involve little redistribution,

–should play a big role in the debate over rising income inequality in the rich countries

The Great Gatsby Curve has made the rounds recently, showing that in countries with higher income inequality, your parent’s income does a better job predicting your income.  One version from Chrystia Freeland, author of the new book Plutocrats (source: WonkBlog):
[Wonkish: Yes, it’s elasticies not correlations. Maybe that matters, I doubt it.]
Testable hypothesis: One reason welfare states are smaller in high inequality countries is because moderate to high income voters demand less government-mandated insurance in these countries.  Most voters in these countries don’t see much point in a wide-reaching welfare state since most voters face little genuine likelihood of falling to the bottom.  
If the Gatsby Curve is right, and if inequality continues to rise, the political support for redistribution will probably fall among the top third to two thirds of the income distribution.  When low income people become The Other in the minds of the median voter, the redistributive welfare state faces a tough political climb.  

Coda: I’m trying to get in the habit of often using “productivity” instead of “income” or “earnings.”  I use the term neutrally, referring to private productivity not overall productivity, so a successful raiding party is just as productive as a McDonald’s.  

Subcoda: I saw Freeland speak about her book earlier this year, and she places substantial weight on productivity-side explanations for the rise of the new plutocracy.