The reasoning you're using is very flawed. Yes, we'll never get to a state where a small number end up with 100% of the wealth. Yes, there will be an equilibrium reached between the wealthy and the middle class. But this equilibrium point can shift more and more towards the wealthy. In fact, this has already been happening in the past few decades, as illustrated in books such as Capital.

And as this equilibrium shifts in favor of the wealthy, you'll see the effects of inequality get more and more exacerbated. You might even get to a point where the inequality is so extreme, that the "masses" have much more to gain through wealth appropriation, as opposed to wealth creation. And when that point comes, democracy will collapse and give way to a communist or fascist revolution.

Basic income offers an escape valve to the corrosive effects of inequality. It distributes more fairly the fruits of globalisation and automation. It gives every citizen a share in the national prosperity. It gives us all a reason to cheer for the greater good, and not just our own advancement.