One of the aspects that is sometimes overlooked is the impact of academic ability on people's prospects in life. People do not start from the same base level of ability. Comparing children from similar backgrounds, it is evident from a young age that all children develop at different rates and have different ways of thinking. "Good" schools will support all children to develop their abilities and learn at their own pace. However, even then, some of them will be able to achieve far better results and show a more natural aptitude for certain academic subjects.
It is those children (who have had a combination of support at home and school, as well as having some natural academic ability) who will tend to go on to the best universities and most intellectually demanding careers. Many of those careers really do pay more because there is only a small number of people with the education and aptitude to do them to the highest levels.
There are plenty of children (particularly in less academic private schools) who have been given all the same advantages, but who are not capable of thinking and performing in the way that is needed for some professions. They are the ones who tend to use family contacts / money in order to set themselves up in privileged careers but not necessarily ones where they will earn huge salaries.
At the other end of the scale are children who have had massive disadvantages that mean that they are already behind academically by the time they start school at 5. No matter their "natural ability", those children will always find it harder to catch up and to compensate for their school or home life. Some manage to do it, but many potentially brilliant minds are lost.
I think that a lot of the people who see themselves as deserving of their high paid careers are the ones in the first category above - they compare themselves to their similar circle of peers and conclude that, because they have always been the highest achievers and possibly worked harder in exams etc throughout their lives, they are deserving of their success. Even if they appreciate that there are huge numbers of people who were born with the same "natural" ability, they might think that certain disadvantages can't be compensated for at the stage of university or when starting a career. The number of "lost" brilliant minds means that there is a smaller number of people capable of doing certain jobs, and therefore the inequality becomes increasingly entrenched.