It's very important to remember that we should not punish the 99.9999% of people based on the obnoxious immodesty of a select few. Even the well-off are likely to need to dip into their reserves occasionally, especially when you consider that the well-off do risky things like give some teenagers $100k so they can try to start a website that might make money some day.
The real problem is not private ownership, which necessitates that at some level, some people will always have more resources than others. The problem is that we've set up an artifice that grossly over-values certain contributions.
For example, the government has created an artificial monopoly on the usage or representation of most ideas, which curtails their free use in the marketplace for hundreds of years. That's bad! As good as ideas are, they are not that valuable, and if we truly believe someone is a genius who outputs unparalleled ideas, granting them a multi-generational monopoly to display facsimiles of those ideas hurts everyone because it actively discourages those geniuses from contributing more for the remainder of their lives. Copyrights are not real property and they must be modified to better represent their value.
Look at the Fortune 100 and think about how many of those companies are there just because the government has given them the exclusive and practically eternal right to resell the same ideas.
Compare Disney, who makes most of their money copying and pasting three semi-concentric circles and suing anyone who does the same, with peers in the top 100 like Walmart and Exxon. Those companies run extremely complex, high-overhead operations that require the daily labor of millions of people to generate new value that assists in fulfilling the population's basic needs. That's the kind of company we should expect to see at the top, not the people who loop re-runs.
Also consider the stock market. There's very little about that which isn't artificial and rigged up and down half way to Sunday. People with 0 involvement in the company can throw in money and watch it grow with 0 input or value contributed, other than already having money. The need to convince people who have been successful that you're a valid investment is a good thing, but we've definitely taken the rewards on this too far.
Such gross misvaluations are primarily enforced by legal actions that codify the mismatch between true value, which the market usually converges upon in a fairly reasonable time period, and the resources the contributor is able to reap for the contribution.
So if we want to be serious about fixing inequality, instead of suggesting forceful confiscation, redistribution, disinheritance, and the creation of taskmasters to make sure everyone is working enough hours, we should look at the places where the market's natural ability to converge upon a fair and reasonable value is being stymied and perverted by profiteering middlemen.