For sure. And I'd add that the acceptance of inequality as a reward does not imply anything about inherited inequality.

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.