> almost everyone thinks they are an above average performer.[...]Therefore, if salaries are shared, at least two thirds of your workers are liable to be pissed off at what they are making, even though the amount is completely fair based on their actual worth to the company.
This is a strawman. Where is your data to back up that "almost everyone thinks they are an above average performer"? At least anecdotally I've never run into anything close to that. Almost everyone I've ever worked with that would be considered at or below average knew very well where they were. Their managers also had the data and would sit down and discuss it with them so even if they thought they weren't they certainly knew the company felt they were.
Perhaps if you jumped into an organization where feedback wasn't given (or given honestly) and opened up salaries you could have an issue. But the majority of companies should be giving employees valid, data-backed feedback which would not make them surprised if someone better performing is making more money than them.
Buffer[0] seems to do well with it and an experiment where a Plumbing company[1] did it ended up having lots of positives out of it. Those are just two data points but it shows it's doable. If you have data that shows otherwise, especially for the numbers you made up, feel free to post it as I would be interested in it.
[0] https://open.buffer.com/transparent-salaries/
[1] http://www.thesun.co.uk/sol/homepage/features/4422455/Pimlic...