It's almost like trying to argue that doctors shouldn't heal their patients because it would be too upsetting for them to change themselves. How about we give them the information they need to learn how to make proper evaluations of their situation? Yes people can be stupid about things. But keeping information from them is not the cure for this, it is the cause. People would not be so concerned if they were part of a professional culture which rewarded them for responding maturely to such discrepancies.

If team cohesion breaks down because pay information is revealed, give them pay cuts for being petty and disruptive. This is not an unsolvable conflict. People are not advantaged by remaining ignorant of their status in a transaction.

>I like the privacy of my coworkers not knowing my exact compensation, it is not their business.

It is their business to conduct the business of the company which employs them, which includes the distribution of that company's funds. Maybe people in other companies don't need to know, but people in yours do, because it is their business.