Sai, your heart is in the right place. Unfortunately your economic theory is not. Who gets to decide who are "legitimate billionaires"? You? Because that's an impossible task by definition. Each person has a set of values that will affect the decision.
Is Bezos a cantillonaire? Not by my definition, he has recreated the world's commerce and deserves his riches. But I've read that many of his warehouse employees need coupons to make ends meet. Unfair in any book.
The only solution: take the money printer away from politicians, and cantillonaires will go away. BTC doesn't fix it all, but does fix this.