Plausibly, if those at the higher end have wages clamped, and those at the lower end can see what they could be worth, wage spend becomes a mean reverting process except with a downward trend driven by a company’s general aversion to spending money.

From the employee perspective, it is of course more fair to be transparent about wages. I personally believe it’s for the best, at least socially and for worker’s rights. In some sense it can lead to worse outcomes, but these are really a reflection of the profit-seeking behaviour of companies, which is also made more effective by wage transparency. I would rather try to fix the underlying issue than not have wage transparency.

"We find that in markets with high individual bargaining power (low unionization rates), pay transparency mandates lower average wages around 2%, as we find in the context of the U.S. private sector. In markets with low individual bargaining power (high unionization rates), pay transparency mandates have little to no effect on wages."

This seems to not be an argument against pay transparency so much as it's an argument for unionization. Transparent prices in any market are important for market efficiency, and that's no less true for the labor market. The mechanism for decreasing wages is "employers resist issuing individual raises because they think everyone else will want a raise too", and that's a cultural thing that will pass in a few generations. I have worked on teams with plenty of people who made more than me, and I didn't take it personally because I knew full well how brilliant and hardworking they were.

This study is a great example of p-hacking and a very poor example that wage transparency affects average pay.

For a counter-example: wage transparency has resulted in runaway salary inflation in athletics, entertainment, tech, and executive salaries.

The point is that wage transparency enriches all of the players, not just the good ones.

With transparency, the information may not be able to capture the differences in expertise of each worker - like "someone who has delivered x products and is well versed in techniques a, b, and c". The market will just show a blanket designation giving an impression of fungibility (which unenlightened management already have) and the tendency will be to push rates down to the lowest common value.