This has been a major concern for many philosophers. Few think that "equality" as an abstract term is ipso facto (by itself) something good; it would not be good, for example, for all people to have the same sickness or ingest equal amounts of poison. But with respect to some domains like moral and legal rights, equality has often been seen as a virtue (you and I should have the same -or an equal-- right to vote, etc). Probably one of the most vexing issues of inequality today --globally but certainly in the USA and Europe-- is the inequality of pay due to gender. There is evidence that men are paid more than women, both in the sense that men have more high paying jobs than women, and in that men are paid more even when they do the same job as women. The American Philosophical Association strongly opposes such inequity and condemns discrimination on the basis of not just gender but sexual orientation, race / ethnicity, religion.
Your focus on the inequality of persons with respect to factors that are beyond our control has concerned some political philosophers like John Rawls and some ethical theorists like Thomas Nagel (one of Rawls's students). Rawls developed a theory of justice that sought to insure that those who are most disadvantaged in a state would receive some compensation; he opposed a libertarian state in which those with natural talents are entitled to maximum benefits without any responsibility for the dispossessed or those worse off. Nagel has spent some time examining what is known as moral luck: cases in which we might praise one person for some talent or virtue or event that was not due to her own free choice but a matter of luck (factors beyond the agent's control).
Unfortunately, there is no consensus on such matters, though I personally commend Rawls's effort to oppose a completely unchecked free market economically and Nagel's effort to distinguish between cases that are and are not under our control. Bernard Williams has also addressed the nature of moral luck. Two other historical, philosophical sources you might look into: Thomas Hobbes's notion that in a state of nature, all persons are equal and Descartes's thesis that all people have an equal ability of use reason. Your last point about the danger of seeking "absolute equality" seems right on. On this point, Medieval philosophers often stressed the good of diversity, diversity of the kinds of creatures that exist and diversity within those kinds. Many many medieval philosophers endorsed a principle of plentitude, arguing that an all good God would not have created a homogenous cosmos, but one in which there are indefinitely many different (and thus unequal) creatures.
See Arthur Lovejoy's The Great Chain of Being for some great references.