If there were no billionaires to look up to, that's a signal that I can't really improve my life much, so why try hard?
I personally strongly disagree that one wouldn't try to improve one's life unless forced to by difficult circumstances. I think we have sufficient evidence that humans are innately curious and creative, and find self-fulfillment in pursuing their curiosity, discovering new things, and otherwise "improving."
It's actually fascinating to me that you have the view of human nature that you do. I don't think this is the right thread to discuss this, but in general I'm very eager to explore that further.
As long as there is value to humans in exchanging different types of resources, I fail to see how economic inequality is unavoidable. We can argue over the appropriate degree, but some level of inequality seems fundamental to the nature of our universe.