Should everybody have equal opportunity?

Should everybody have equal opportunity?

I found myself contemplating this question after inadvertently stumbling across the apparent dichotomy between the two senses of equality: equality in opportunity and equality in success. The former is a belief that no one should be born with an unfair advantage, the latter is a dogmatic creed that holds that everybody's success should be put in parity with each other.
But before we move on, it must be noted that it is eminently clear to anyone sufficiently grounded in reality that equality does not, will not, and cannot exist in any material sense; everyone is different, no human being is equal in ability and action than anyone else. Mind you, this does not mean that anyone is intrinsically superior to another, but simply that no two individuals are equal.
Going back to the question of whether people should have equal opportunity or not, it seems to me that individuals manifestly do not have the same opportunities as each other, a poor kid will most likely have less opportunities than a rich kid, for example. The problem arises whenever an intervening entity, such as the government, elects to disrupt the natural tendencies of reality by directly eliminating the inequality of opportunity that necessarily exists as a part of the human condition. This usually involves programs such as welfare, the progressive tax, affirmative action, and anti-discrimination laws. But because it is based on a manifestly nonexistent concept, state-imposed equality is a failure that is doomed from the start. And in the process, it systematically eradicates all of human liberty.
So the answer is no, people should not have equal opportunity because it is an empirical absurdity, the only way it could conceivably exist is through the actions of an unlimited State that controls every human action. Equality of opportunity should only exist in the sense that the State should have no right to violate the individual's right to life, liberty, and property.