Separate questions:
(1) Should we accept some level of economic inequality in society?
(2) Are the wealthy more "deserving" of their wealth than the non-wealthy?
It's perfectly consistent to answer (1) Yes and (2) No to those questions.
Capitalism is an economic system, not an ethical system. The "invisible hand of the market" is not God handing out rewards and punishment, though some people seem to believe that.
Even if we grant the proposition that a good way for society-wide progress is to harness the desire of some to have superior positions by forcing them to work hard at creating value for others, it doesn't really follow that inheritance is a good idea. Indeed, you could argue that it's just the opposite, if we really want a nation of hard workers, we have to make sure the youth can't get away with being lazy just because of some historic success that they didn't have any part in.
There’s a whole lot that a society can do to address the negative aspects of wealth inequality. Almost all of it means that the wealthiest people will have to make some sacrifices—in proportion to their wealth, *incredibly small* sacrifices—and will have to accept that just being poor shouldn’t be a death sentence, that everyone should have food, and water, and housing, and education, and medical care, and transportation, to a reasonable baseline level, simply for existing.
Our species is prosperous enough that no member need ever experience homelessness, nor hunger, nor untreated injury nor disease, nor unwilling ignorance, nor an inability to pull up stakes and move. The only reason the status quo persists is that it is to a small number of wealthy and powerful peoples’ benefit, not because it’s the best possible arrangement for society.
Did you notice what I didn’t suggest? I didn’t suggest that the rich should lose their wealth or position. In fact, they don’t even necessarily have to pay more in taxes than the middle class. They just need to pay around the same *proportionately* as the middle class.
The top 20% of earners pay more taxes than the other 80% of earners combined.
This is due primarily to the total amount of their earnings rather than their tax rates.
It’s saying “Because this person is a Jones, they deserve a spot at Yale even though others are more academically deserving, and we will pay you for that privilege.”
This is also why grade inflation happens at these institutions: “You can’t fail him, he’s a Jones!”