The old and the rich are the same. People over 55 own 52% of the US which is one of the best examples of inequality. Boomers all together own 8x more than billionaires. Any old person with a decent 401k or otherwise stock/index fund based retirement is one of the shareholders living off the working class.
After the billionaires are guillotined or otherwise disposed of, there would still be terrible inequality that needs to be taken care of. Put simply, the billionaires alone don't have enough assets to fix this.