Remuneration should be commensurate with the knowledge, skill and level of experience required (and delivered). Those criteria determine the scarcity of alternative candidates, and therefore the difficulty of replacing an incumbent. The more difficult to replace someone is, the more they would get paid to try and stop them leaving.
Now, that is the theory but in practice that's not always the case. Plenty of people leave to go into jobs with lower pay but have a better quality of life, shorter commute, better company culture etc etc.
However another factor has to be accountability. As a junior member of staff you have less accountability than as a director etc. They ultimately take responsibility at a much higher level and should carry the can for failure. As a result of the responsibility and accountability that goes with it there is a higher level of risk to the individual's circumstances so it follows that higher pay is required. The issue seems to be that the accountability often just is not there.
Salary as an indication of ability? To an extent, yes. But also as an indication of political savvy, networking, bullshutting, negotiating ability and of course, experience. Remember some people don't necessarily want to climb the ladder, for example somebody at a legal firm may just want to be a good property lawyer, but not be a good salesperson. They therefore may not climb the latter to the top echelons despite being a very good lawyer. They may not get the megabucks for bringing in business, but they are doing something they are good at and enjoy.
In terms of public v private sector, it's very hard to compare. It would be very clichéd to say they attract a different sort of person, but in my experience you do encounter differences although the same is true even within the private sector. The argument could be made that a council executive has much less accountability than, say, a director of a FTSE 100 bank. Also there is the case that a public body is likely to want somebody with public sector knowledge, who is well versed in the ways of the council - they would promote within. Therefore it is known what would be a reasonable expectation to get the (possibly already decided) candidate they want. Whereas a large company trying to attract somebody with good knowledge of international cooperation, regulation etc will be coming from a global marketplace with more competition.