Most jobs that truly are "trivially automatable" have already been automatized. I think it's extremely unlikely that most or nearly most of Americans' jobs can be replaced by computers in our lifetimes, barring something like the Singularity happening (which I'm not holding my breath for).
Wealthy people will actually own the means of production in a very meaningful way
Like I said, this is a Marxist bromide. Fundamentally, the means of production is mens' minds. Marx mistakenly believed that production amounted to physical human labor + expensive heavy-industry capital (like factories), which leaves work requiring intelligence and skill (MOST work) out of the picture, and is inaccurate - and is becoming more and more innacurate.
those that aren't equipped by their genes, upbringing, or education to participate in the information economy will be unable to earn an income.
Everyone is equipped to participate, barring exceptionally low IQ. Human beings are not automatons; they are not determined by the environment or their parents or their genes; they exercise choice.
Secondly, despite the information economy, it is still very much about what you own. If you are capable of making something amazing, you still need savings or investors who will feed and house you while you make those things and pay the still significant costs of infrastructure that many products require.
Big projects typically require capital investment, but so what? That can be gotten if you have a good idea. Also, lots of people that work in service jobs and don't need heavy capital investment do important, creative work. My point here is that, no, it's not "very much about what you own." Most people in America are doing just fine, especially those with an education, and most people in America did not inherit a trust fund or something.
Concentration of wealth matters. That doesn't necessarily mean that government intervention is a good idea.
If it has no implications, then by definition, it doesn't matter. So if you claim that it matters, you should give an implication.