A sense of equality is very important for a variety of good reasons. Whether this is more important than equality is a complicated question that is made more complicated by the fact that equality is hard to measure.
True equality is generally rare in a high dimension space. People bring a lot of different things to the table so it is unlikely that two people are doing the exact same - hence differences in pay will always exist. Add to this the fact that people may feel that they are better than average (most people do) and thus entitled to a bump over their peers. Having approximate equality is more realistic. If you accept this, then a comparison against a distribution rather than against a specific individual comparison is a more realistic evaluation.
Verification of parity in compensation encourages equality only if there is a clear mechanism to equalize levels. In general there will be mismatches in market forces, budgets, and the like (as well as seniority, the difference between people's opinions of themselves and their opinions of others, etc...).
Having some ambiguity about such levels is also an effective social mechanism that allows us to see each other as equals without needing to get out a ruler. Again, having an anonymous reporting scheme like levels.fyi strikes me as a very good idea, but open and interpersonal salary discussions strike me as a potentially bad idea.
You know what encourages equality? Open verification that there is actual equality.