Small businesses are unlikely to host billionaires. The problem with billionares in a mixed economy is that they are likely to have not done that much themselves and there is a chance they just found a way to hack the system (mixed economies are very hackable) and now have more than the world would have without them.
I'm not that mad about it but I admit a world of billionaires controlling most areas of the market can be a sign that the majority were restricted from competing at full force and one person found a way to cut through that.
So why don't we restrict people less. Why don't we ask the kind of people we want to succeed who's businesses would compete with the billionaire and drive down prices for us which restrictions would produce the best impact for them if they were removed?