Your financial planners exercise was off the mark for me, but then I have a wide range of close friends. The "artists" throw the equation way off.
For me, I will feel "wealthy" once I hit that stage Gates is referring to, when anything beyond it is simply gravy. When I can safely say I no longer need to work to earn money, the money is doing that itself.
Regarding the management of finances, I am horrible at it. My wife is fantastic at it. I'm good at making money, she's good at managing it. It's a nice symbiotic arrangement. I work with a guy that is fantastic at managing his finances. At 30 he already owned 12 rental homes. He lived with his wife and son in a very modest home and bought other modest homes and rents them out. He buys 2-3 houses a year now. Because they are extremely frugal, he is able to do this.
He recently asked me about my iPhone. He was considering getting one but thought they were too expensive. This guy owns north of 15 homes but won't buy a $300 phone and instead uses an old blackberry that he got for free. When I asked him why he didn't treat himself to the "nicer" phone, he took out a pen and paper.
As he was showing it to me, he kept saying things like, "buy an iPhone", then he would draw the arrow further, "buy a boat", then he would draw the arrow further, "buy a sports car", etc. He has done the math and by the time he is 38 he can have 25 homes and enough passive income to live very comfortably and continue to reinvest in more houses. I don't have his discipline, but my wife does (thankfully).
So his definition of wealth or being "rich" is the day he can stop "working" for a company and just manage the properties he has acquired. His definition is not measured against his peers but is measured against a goal he has set forth for himself.