Inheritance is an advantage. Sure but it's an advantage of outcomes not one of opportunity. That's all I'm saying.
My parents were poor immigrants who became wealthy through hard work and the glorious advantages America has over Central America and the West Indies. The advantages that they pass along are far more useful while they're alive than the value of any inheritance (although that will pretty much mirror your grandfather - places to live rent-free, paid education for generations coming down the line, etc.). My wife comes from a similar background (except her parents aren't immigrants, they still live overseas although they have properties here too).
But most of those advantages arise from how the wealthy choose to spend their money. It doesn't have to be inheritance, it can be a trust or some other wealth transfer vehicle. And that's why reducing it is more about reducing inequalities in outcomes, not opportunities. People who became wealthy can spend their money to give advantages to whomever/whatever they want (sport teams, college they attended, etc.). Reducing the amount of money they can spend after death is about limiting the reach of their life's outcomes.