Why are people rich? Different people become rich for different reasons, such as:


Developing/selling a great product 
Investing
Winning the lottery
Inheriting family money


Some of these seem more fair than others, which leads me to wonder: Are there any studies that attempt to measure what percentage of people get rich in different ways?
You have some incorrect ideas about wealth. First of all, inheriting money does not concentrate wealth, it disperses it. Usually the recipients of inheritances, both organizations and wayward children spend the money the receive so the inheritance is dispersed completely.

Most people who are wealthy got that way not by earning a lot of money, but by saving the money they did earn. How much a person saves and invests is a much bigger indicator of wealth than income. A plumber that saves and invests will eventually become much richer than a doctor who spends all his money. 

Also, most people who wealthy are not manufacturers who "make a great product," they are ordinary professionals and businessmen: doctors, lawyers, business executives, electricians, plumbers, and builders. You can even find many blue collar workers who have become rich by saving and investing: policeman, firemen, teachers. Where I live there are two teachers, a husband and wife couple, who started out as ordinary high school teachers and now they are quite wealthy and own their own private school. There are probably more millionaire garbage men, than there are millionaire manufacturers. Owning a bunch of garbage trucks is enough to make you a millionaire. Now think how many garbage trucks there are.

Here is an article about typical characteristics of wealthy people:

https://www.nytimes.com/books/first/s/stanley-millionaire.html