> most people gain wealth by running successful business

In the USA, this is absolutely not true. The majority of the 1% earn their wealth through inheritance and investment, not running a business.

> if they instead inherit that wealth, there is nothing shameful about that either

Depends on whether you consider inter-generational wealth transfer completely valid, or the basis of most oligarchies. "I'm rich because my parents were rich" is thing that the US accepts as almost god-given, but it really is not if you look across time and space. The idea that I should just be able to transfer whatever wealth I have upon dying to my children is an idea very much promoted over the last couple of centuries by the wealthy, and is not "the natural order of things" (because there is no such natural order).

>> The idea that I should just be able to transfer whatever wealth I have upon dying to my children is an idea very much promoted over the last couple of centuries by the wealthy, and is not "the natural order of things" (because there is no such natural order).

Inheritance was a thing in ancient Egypt 5000 years ago and probably from the beginning of humanity (if every generation had to start from zero, we would still live in caves).

> if every generation had to start from zero, we would still live in caves).

We're not talking a generation starting from zero, but instead specific children within a family. If the wealth left over at death went to the state, the "generation" would not start from zero (and being realistic, it's not that likely that the deceased's offspring would either).

Also, inheritance may have been in ancient Egypt, but so were death taxes. Similarly for the Romans, and feudal Europe. Not that the rulers collecting these taxes were exactly the personification of righteous and just government.