Seeing how the right to privacy is not specifically enshrined, I would argue that the reasons for keeping some things private is very much at the heart of the matter. For instance, why does the government not think the benefits of transparency outweigh the disadvantages when it comes to individual reported income, versus say, divorce records (most of which will include income, among many many more private facts said in court).
Like most implied rights, the right to privacy is weak specifically because it is not enshrined. Even the explicitly stated rights have limits, particularly when they butt into the other explicitly stated rights.
When the implied "right to privacy" butts into the 1st Amendment rights of freedom of expression and a free press, on which side do you think the courts will err on, on a consistent basis?
The state has gained an absolute right to know your wage, which one could argue that abolishes the private nature of that information, much like your gender, or your face.
I know plenty of people with cars that cost 10x the price of mine, who earn far less than I do.
And outside of their immediate industry most people don’t know other salaries, or how to look them up.
If an programmer makes $100,000 in a company where programmers regularly earn that, it should not be public information. If the programmer is earning $2 million, it may be material to the shareholders to know that depending on the size of the company. If the company is Google and the programmer is regarded as extraordinary for some reason, $2 million (vs Google's overall financial picture) isn't a huge sum. If the entire sales of the company are $30 million, it blatantly would be material.
The most obvious argument against it, is that people aren't always rational (and are regularly irrational about things like money). I'd argue they frequently aren't able to accurately assess their own financial value (in either direction). It opens a pandora's box within corporations about why X person is worth $Z, while Joe or Jane thinks they should obviously be paid more vs X person. It's not easy to maintain harmony within organizations, that would make it far worse.
What would be the value gained from making all individual employee salaries public (within a public corporation)? It would have to be immense to offset the friction it would cause.
Compensation is an important conversation to make sure a job is a win/win. I think "What would you like to be paid?" is the most relevant question anyway.