Can you elaborate on why do you think that it "would place significant downward pressure on my salary" ?
I agree that in a particular single negotiation if it just so happens that they have this information then it could be a significant impact one way or the other (depending on what that history is) - especially since there's an information asymmetry since they know what you're making but you don't know what their other employees or the other applicants are making.
However, if it's a policy so that this information is available for both sides in every negotiation for everyone then it doesn't seem that this should fundamentally change the average pay in any industry. The core supply/demand factors are the same, and for every instance that might lower the wage there's are many cases that would have an upward pressure, i.e., the underpaid people can now objectively see which other companies pay better, and such employers can't simply rely that long-term loyal employees will be ignorant about the market rates as they do now.