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For a job whose going rate is M, a company would offer N to Bob and N-d to equally qualified Alice. If they want to hire Bob, they have to publish that they offer N so he applies. Now Alice knows that something is up when they offer N-d.

Theoretically this pushes d toward zero. M and N, I don't know.

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Except they post pay ranges and not a single salary. They could just make the pay ranges really big and use the ambiguity to avoid the intended effect

Also I have no clue whether it actually helps reduce pay gaps on average. I remember reading a study in either Australia or UK (can't remember where sorry) where it had the opposite effect

Better information should in theory help with problems caused by lack of information. How it's implemented makes all the difference, of course. I have no idea what if anything this law will actually do.

If they’ve been getting away with paying women less, why don’t companies mostly hire women to save money?

I get the sense you want me to defend a broader position. I was only answering that one specific question about why they mention d.

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