Being a billionaire has very little to do with you. It is more a testament to the wealth of your parents, the gender you were born in, the colour of your skin, and luck. I have no doubt many possess wonderful qualities too, but that doesn't set billionaires apart from the rest of the population. It's what makes them a part of it.
There are some billionaires who inherited their money. There are some who lucked out with investments. Your last statement makes no sense. What sets them apart from the rest of the population definitely does involve their "wonderful qualities".
Sure, luck plays a big role in things. It takes a combination of other things too: hard work, an unwillingness to settle for "meh, good enough", an ability to convince other people (employees, investors) to believe in you and the ability to know your own weaknesses and bring in people to solve those weaknesses. Let's not just lump these all into the "and the rest" category.
It's easy to credit them with hard work and think they deserve it. The biggest thing I notice is how many thousands (millions) of other people in the world have the exact same traits ("Seeing past the trees", "Ability to convince other people to believe in you", etc) and fail in our world.