Everyone knows they make less than their boss, yet people don't bully their boss. Nurses know they make less than doctors, but they don't bully them. Adjunct professors don't bully full professors. So we can "handle" non-transparent pay when its built into job duties and titles, so it's not that much of a stretch to extend it to employees with similar job duties and titles.
The government sector already has transparent pay and ~17% of private companies have transparent pay, yet we don't see bullying there.
In fact, some preliminary research suggests employees feel more valued and feel their pay if fairer when there is pay transparency. When people don't know what their colleagues are making they tend to assume they are being underpaid.
If you're seeing mass bullying then you've got a problem that can't be solved simply by hiding salaries.
>think of what often happens to the best pupil in the class, where you have "grades transparency"
What? What happens to them? They get to speak at graduation?
The vast majority of adults are mature enough to understand that different people have different work outputs, different value to the company, and therefore have different salaries. We also are mature enough to understand that tenure and seniority are rewarded. We already accept that people get promotions at different intervals, and we already accept that only one person gets the "employee of the month" parking spot and spot bonus.