People value transparency, and it might be that they would prefer a lower salary at a more transparent workplace.I specifically said above, "Where the cost analysis may not be the same for each side.". This obviously includes non-salary benefits (stock, vacation, flex time, home life balance, etc).
You are also only addressing the workers with below-average wages (who may be qualified for higher pay) when you say that secrecy helps employers.
I specifically said above, "The worst case scenario for the employee is to find out they are making significantly more money than their coworkers, in which case they have no further bargaining power.". As an employee, your bargaining power is not reduced if you have knowledge of that you are paid above the median. In other words, from the employees perspective, there is no situation where you are in a worse negotiating position due to having more salary information.
so I would assume that transparency could be used to bargain them down, as the below-median workers were helped in bargaining-up;
Note that when negotiating, the only party that is going to negotiate for lower wage is the employer (since it is generally unlikely that an existing employee is going to ask for a lower wage voluntarily). And from that position, the employer already knows all current salaries. If you are making substantially more than the other people, then the employer can (and likely would) reveal that information in order to help secure a lower raise (or also likely, no raise, and unlikely, a lower wage). That's the power of information asymmetry. The employer can use the information when it benefits them (reducing the size of a raise for an already high compensated employee), but withhold that information when it does not benefit them (when a low compensated employee is up for a raise).
don't know why we should assume it goes one way or the other.
We don't have to assume anything. This is basic economic and negotiating tactics.
I am not an advocate for wage transparency or opaqueness, because I don't know which way the effects go for anyone.
It's perfectly reasonable to have an opinion on wage transparency, but it seems a little odd to say "I don't know which way the effect go for anyone". We have negotiating models and frameworks specifically for this type of activity. And the general rule is, "The more information asymmetry that you have in your favor, the better your bargaining position". Specifically because it allows the party with the additional information to use that information when it benefits them, and withhold that information when it does not benefit them.