In fact, the whole American system is built to prove the opposite. Space at the top is NOT limited.By definition, it is. The question is whether one focuses on absolute or relative prosperity. Like you (I presume) I also prefer to focus on absolute prosperity because nothing can be done about relative prosperity's zero-sum nature.
However, it would be good to see less inequality. I'm not a hard-line "everyone-should-have-the-same-amount" egalitarian because that's a terrible idea-- people would lose the incentive to do the work that society needs-- but inequality has gone far beyond the point of being valuable or productive. Now it's just self-perpetuating and exists for no other reason.
Total wealth is NOT limited.
Sure. Unfortunately, the vast majority of people (95+ percent) end up working below their ability (a loss to them, and to society) because they lack the scarce social resources, credentials, and connections that have congealed "at the top". There are also inefficiency problems in a low-mobility society where (as we now see in the US) the wrong people are making the decisions.
Anybody who works hard (and smart!) can get there.
Total bullshit.