There is no significant problem with billionaires or similar. I know this is going to be an unpopular opinion but unless you are going to chuck out capitalism then concentration of wealth is an inevitability. I would in principle be all for that, but that isn't a reform, it's a complete economic revolution and I don't see it happening any time soon.

The actual solution is 100% inheritance tax. Or maybe limit it to something like 2x median salary, and use the extra tax revenue to give that much to anyone who doesn't inherit that much from their parents when they die. Promote actual competition with a more level playing field and significantly diminished unfair advantages. It does not solve everything but it is a huge step in the right direction. And it gets old people spending their money as they can't take it with them and they can't leave it to distort the world in favour of their offspring.