I think capitalism needs some amount of inequality to work*. A smarter, more knowledgeable, and more connected person needs the power to command others to bring her or his ideas to fruition. Allocating capital to those who have earned it through experience in the workforce is not a bad way to do this, since it's possible to learn a lot about a field by participating in it. (Of course, this isn't true for most jobs, which are mind-numbingly routine. Automation and minimum wage had a chance of saving the working force from this, at least until business leaders decided they'd rather export jobs to countries they could find workers at essentially slave wages.)
Ideally, it would be possible to mitigate the negative effects of inequality. However, in practice, this seems mathematically impossible, basically because of the principle that says the "rich get richer", and the negative aspects of inequality become unbearable amplified.
That's not to say that there aren't other possibilities. Obviously what we have now is far from optimal. Efficient market hypothesis--LOL. And I'm not saying this with Soviet style communism in mind for comparison; just look at the debt that Silicon Valley has to project Project ARPA, Project MAC, SRI, etc, all of which were funded in large part (to my knowledge) by a government agency connected to the U.S. military, and some university campus like MIT, Stanford, University of Illinois, etc.
Also, I'm surely biased, since I'm focusing on what is most familiar to me (software). I'm sure that the extent to which any amount of inequality is desirable depends on the sector.
Finally, I'll be the first to admit that in all of this half century of software entrepreneurship, we still haven't realized the vision of the people at the AI labs of the early `70s. Just compare the web to Engelbart's "Mother of all Demos"--the web is a joke in comparison. What we have now is incremental improvement on a half-century old idea, but with the wrong people getting (ridiculously) rich from old ideas in the process. Take Google, for example: Pagerank essentially made sense of the tangled mess that was the early web. Does it make sense that the web was implemented in a way that required a private individual to recognize this, and create a solution by his own wherewithal and connections? In the early days of Google, bandwidth used by the site consumed a considerable amount of bandwidth from Stanford's campus internet. In the end, Stanford benefits from alumni like Brin and Page, who ultimately pay back the university handsomely in direct contributions, and indirectly in all sorts of ways. Does it make much of a difference that Google, rather than a government lab or university, is doing a lot of the cutting edge research in computing today? Perhaps, because, although I'm sure Google employees carry a lot of the knowledge and experience gained there in their heads, the majority of it doesn't get released to the public. And the chance to be a Page or a Brin is more or less a function of inherited wealth and academic lineage. It sucks that 99.9999% of people are denied this by birth, but the laws of the physical universe aren't based on human ideas of morality and fairness. OTOH, if you happen to have a really high IQ and get into Harvard, you have a shot at meeting the classmate with whom you'll start the next Facebook, but if you can do this, then it means you've either inherited that IQ, or benefited from the high IQ of your parents in other (probably more important) ways. So, inequality also extends to the genetic level.
* Another example: the more wealthy consumers who purchase high-end products push forward technology, and (potentially) increase employment of researchers working on cutting-edge products. Of course, the same process could take place in a university or government lab. In addition, there is always the scourge of patents.