Anti-trust law hasn't (yet!) destroyed Google - however splitting up monopolists like Standard Oil or various cartels seems a clear win.

This has more to do with failure to enforce anti-trust laws in a meaningful way, though. In the case of Oil and most major cartels, these are not natural monopolies: they are monopolies built and maintained with the express help of various world states, which is a somewhat different matter.

Inherited wealth certainly does harm you. You and I are not on a level playing field with the son of some Saudi prince. We cannot compete fairly for jobs, or wealth. Its not 'caring for them after they're gone' its giving them an unfair advantage over the rest of us.

Economics is not a zero sum game. I doubt I'm going to find myself competing for a promotion with a Saudi prince. Rich people do not harm the poor with their wealth: they simply may not help (aside from, say, putting their money into banks and loaning it out to less wealthy people).

The education point follows from this, since purchasing better education is perhaps the primary way people inherit privelege. Education in our present society is a positional good - its distribution is zero sum. Some rich woman buys an extra qualification for her daughter, your parents can't buy it for you, she gets the job - not because shes better, but because her parents are richer than yours. Certainly hurts you.

Knowledge is certainly not a zero sum game! Besides, if you genuinely want everyone to have an identical education, you can't simply provide public education - you must also outlaw private schools, home schooling, and any sort of parental involvement in education: after all, why should the child of a college professor have an unfair advantage over the child of a ditch digger? That hardly seems fair.

My perspective here is colored because my public school experience was more or less entirely catastrophic, and I am predominately self-educated. If we were to force everyone to be educated at only modern public school levels, it would be an economic and cultural disaster of hard-to-register proportion.

So perhaps the type of information campaign needs the public backing of government, as this carries the legitimacy of collective action. Also, if we start from now, the 'private organisations' with disproportionate wealth and power will be able to produce more propaganda and preserve the status quo (that benefits them)

Large charities also have the 'legitimacy of public action.' Also, if you think the government won't use its propagandizing power to preserve the status quo that benefits it, you've never sat through the pledge of allegiance.