Efficiency is about producing more of what you like, while keeping as much of the stuff you like that has already been produced. Whenever it's brought up like you have done, it's always an ideological point to some extent, because "what we like" is not well-defined. If I define inequality as a "bad," and capital as "not necessarily a good," then an exchange of inequality for capital is not efficient.
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.
There are so many weirdos living in their little political fantasy bubble that I can't even tell if your post is satire. But in case somebody comes up with an equivalent but more serious looking argument than "living in an aluminium box with no aircon and eating over my own toilet bowl? I'm kind of jealous!" or "the successful should be rich, ergo the less successful should obviously have any dignity stripped from them", let's offer some counter arguments:
What rates a society as a Third-World country is not its absence of super-rich (most countries have these) but its absence of a middle-class. So by your own reasoning Congo and Angola, with their tiny billionaire class ruling over starving millions, are "super efficient". I'm sure you'd enjoy living there and the rest of the world should be kind of jealous.
Anyway. On a more grounded note, in the realm of people who rely on data instead of sophistry, inequality is considered economically inefficient, even by historically free-market organizations like the IMF and OECD:
https://www.economist.com/blogs/economist-explains/2015/06/e...
https://www.forbes.com/sites/eriksherman/2014/12/09/income-i...
Was that a (understandable) dig at praxeology? :-)
Put down the Ayn Rand fantasy novels and go meet some people outside of your economic bubble. Not everyone can be a software engineer in Western society. I'd wager you're about as responsible for your lot in life as these people.
Read about the history of the industrial revolution. Tenement life in NYC. Try to empathize. Develop some humanity and real perspective for Pete's sake.
By the way, no one is stopping you from living like that if you're so jealous. But it's clear you wouldn't last a day like that, you're all talk anyway.
And even aside from the obvious moral problems of extreme wealth inequality, it's not even economically efficient. You can't have a strong and growing market economy without a middle class. Hong Kong could get away with it for some time because their economy is based on international trade and finance, but that only takes you so far. Eventually you need to develop a domestic consumer base. Their current political crisis is caused by this inequality catching up to them, though the HK business and political elite conveniently pass the blame to Beijing.