But more importantly, they had these traits and also got exceptionally lucky. Having self discipline, perseverance, and a delayed gratification mentality is no where near enough to become wealthy.
Not true at all. Investing a small sum regularly over time can lead to wealth. For instance, investing $300/mo in a mutual fund like Vanguard Total Stock market (historical return 9.72%) over the course of 30 years would yield a market value of $644,124. Edit: Which would be considered wealthy by a lot of people. Not 1% rich, mind you - but plenty to live a comfortable life. Just imagine if you were able to put away a little more, a million dollars is not far-fetched or out of reach.
I think it's important to understand money; and even more importantly, the time value of money, to become wealthy. Lots of people who understand that can become wealthy - almost irregardless of their income.