In the USA, the broad range for federal public service is defined for GS-1 through GS-12 or -13 (I forget how high they go) and GM-9 through 16. But the bands within range are less public, and even the bands have a non-zero range to them.
However, NO. The problem would not go away with time as long as the issue includes performance or productivity and the perception thereof. (The writer in me just clicked on the alliteration of public perception of performance and productivity pursuant to pushing promotions.) It DOESN'T MATTER what the ranges and bands are. What matters is how fast you advance through them. And as long as a person's ranking within a department is part of their PRIVATE personnel file, the reason that person isn't at the top band of GS-12 is not visible, nor should it be. It is always a matter of motivating the person without exposing their shortcomings to the rest of the world.
I could imagine a review board looking at promotion history for a department head to determine if any obvious bias exists. But as long as there is a cause for a person to not be promoted, and as long as that cause is documented in the personnel file, there still could be inequities in salary. And the question then becomes whether the stated cause is correct or not. But as long as there IS a recorded cause, to override the manager at that point completely undercuts that manager, who was hired to MAKE that kind of decision. So now you second-guess and eviscerate the boss, who (for this exercise) wrote down reasons for any given decision?
I have been a department manager with hiring and firing authority. I was one step away from a corporate vice-presidency, though I had to turn it down for personal reasons. I understand the decisions inherent in assigning relative value to employees for the purpose of determining raises, bonuses, promotions, recognition, and the other sides of those managerial coins. Although I was a big rugged at times, I learned how to be equitable and to take personalities out of the equation. If I had any weakness as a manager, it was that I was too kindhearted. With a limited amount of money in the pot for the next year's salary adjustments, it was always a painful balancing act.
Just like USA multi-millionaires find ways to evade taxes, managers will find ways to choose salaries and rewards via personal considerations. They will find the way to evade the glaring light of scrutiny. I've seen it before and there is no getting around it. When a manager is out to get you, unless you have a strong union contract, you can consider yourself GOT.