That completly misses the point, first, rich people earnings come mostly from their investments, not their work. Second, the money earned through investment necesarily comes from the work produced by other people and thats completly independent if the rich person works or not.
The person who "earns by investing and working in both nearly equal proportion" doesnt really exist beyond outliers, this is empirical, the 1% owns as much wealth as the entire middle class, this is where their yearly income comes from,they get money because they own stuff, not by being superworkers, otherwise the inequality wouldnt be growing.
I get the sense that you’ve read a lot of theory without any observational facts.
The vast majority of the 1% and 0.1% get most of their income from labor nowadays. This is a phenomenon called “The Rise of the Working Rich”. This looks like CEO compensation, top athletes, too musicians, business owners, and so on. On average, the 0.1% gets about 20% of their income from investments and 60%+ from their actual labor.
70% of the Forbes 400 are self-made, the vast majority of millionaires receive $10k or less in total inheritance, 11% of Americans will be in the 1% for at least 1 year in their lifetime, and the majority of Americans will be in the top 20% for at least 1 year in their lifetime. If you chop off the top 1% in developed countries, their Gini coefficients are very similar, implying that the US doesn’t have exceptional levels of suffering from inequality, it just produces a lot of rich people.
The person who "earns by investing and working in both nearly equal proportion" doesnt really exist beyond outliers, this is empirical, the 1% owns as much wealth as the entire middle class, this is where their yearly income comes from,they get money because they own stuff, not by being superworkers, otherwise the inequality wouldnt be growing.