It's called taxes, death, and children. Billionaires only have a single lifetime to spend their wealth, taxed at pretty high rates when they actually liquidate their assets, and it eventually evaporates over a few generations.

There's ~3k billionaires and they're powerful enough that they'll be able to avoid those caps through loopholes, like through shell companies. There's no real practical way to prevent someone from accumulating wealth if they wanted to continue to do so.

That quote about no more billionaires is from someone that cares more about making a point than actual policy.