I can imagine a number of downsides to publishing pay rates. Not every workplace is a beacon of maturity and comfortable upper-middle-class wages. Some offices have politics, gossip, and troublemakers.
Immediately employees would be calling meetings with their manager to hear the justifications for pay rates they felt were unfair. This could repeat with each new hire, promotion, raise, bonus, and change in responsibilities. This generates wasted time and increased turnover. My wife's design company would virtually grind to a halt for a few days. Even after everybody is placated with their pay rate, each doling out project assignments would be a new opportunity for friction over who deserves to do what. Then let's consider accusations of sexism, racism, ageism. The number of discrimination lawsuits would likely be non-zero. There are also social introverts who don't want to turn half of their co-worker interactions into awkward conversations.
So once profitable workplaces that kept everybody moderately polite and happy could face several obstacles.
Handing out raises wouldn't solve all of these problems either. I'll admit some worker bees would probably get paid a little more.