It may be true that people with wealthy parents will become wealthy via inheritance, but it is far from being the more prevalent manner in which wealth is attained.
Check the real statistics on this. The number of "self-made" millionaires or first-generation millionaires is much much larger than the number of inherited millionaires. Forbes estimates that 70-80% are millionaires are first-generation millionaires who earned an invested their way to wealth, compare to 20% who inherited significant portions of their wealth.
For billionaires...Forbes:
"Over the past 30 years, the origin of the wealth of the richest people in the United States has shifted away from old, inherited money...In 1984, the first year for which we have crunched the numbers, we found that nearly one-fourth of the members of the Forbes 400 inherited their fortunes and weren’t doing anything to grow them...At the same time, only 2.5% were ranked as 10s, or absolute bootstrappers...The trend began to break down in 1994, when we saw an equal number of inherited and self-made billionaires...Already in the 2000s, our data finally showed a greater proportion of self-made billionaires. In 2004, we had 59% of the Forbes 400 having made their own fortune, as opposed to 41% who inherited it...Thus, the most encouraging results come from this year’s Forbes 400. For the first time in our data set, we see the number of self-made billionaires who rose from nothing, and overcame various tough obstacles, outpacing those that just sat on their fortunes. A total of 34 billionaires, or 8.5%, scored as 10s, or more than three times as many as in 1984. The number of 100% inherited fortunes as a percentage of the total fell to 7%, with 28 billionaires in the 1 category, compared to 99 back in 1984.
Forbes defined a 10 as "To qualify as a 10, a member of the Forbes 400 had to have been raised in a poor household, and have endured extreme duress. Oprah Winfrey, who endured sexual abuse, and George Soros, who survived both the Nazi and Communist occupations of Hungary, are great examples." OTOH, a 1 was someone who inherited wealth and has done nothing with it.