Your second point is an interesting theory, but seems unstable. What if one capital owner decides to consume a smaller amount of his wealth, and thereby increase his share of the economy?
Yes, I'm not saying that's where society is actually headed. It's just a hypothetical to illustrate how r can diverge from capital's "growth rate". To rephrase the last sentence, "In the extreme case, you can imagine a hypothetical equilibrium where..."
Eventually he would rule the world.