Sounds like you're thinking of regression towards the mean. Newborn children probably get a random roll when it comes to financial aptitude as is mostly true with other types of aptitude. Being the son of a skilled investor won't necessarily make you a skilled investor. I think they'd still be above average though since the son of a skilled investor will likely have access to more connections and a better education than the son of a janitor.
This is true, but at the end of the day most wealth created in the US at least is first generational. It's not uncommon for a family fortune to be lost in 2-3 generations.
I can think of not a single family who started out wealthy and lost it all. What's far more common is dilution of wealth. Start out with $100mm, split that 10 ways through inheritance, then split that again, and again. The Rockefellers, Carnegies, Mellons and Westinghouses still exist, just under many different surnames.
If you start out even with $100k inheritance you're pretty far ahead already. That's enough to get an education, buy a home, or start a business. If you can turn that $100k into $1mm you can draw off $35k for the rest of your life without lifting a finger.
Having modest savings and being in good health makes you much closer to wealth than if you were further down the economic chain.