This is the Central Limit Theorem at work. Your random variables are independent and identically distributed so you're always going to approximate a normal dist

This is the Central Limit Theorem at work. Your random variables are independent and identically distributed so you're always going to approximate a normal distribution. Wealth in real life is not independent. People with more wealth have more investment opportunities and thus more ability to grow, tending to a power law. You can see the same phenomenon with craters on the moon.