That's one way, at least, where neither party has to concede the information advantage.
In fact, I'm surprised there aren't already 37 start-ups that offer this as a service. You could have a cute little envelope logo like the MS Outlook logo and give a TED talk about how you're totally disrupting information asymmetry in recruiting, and eventually be pressured by techtopus to provide data about what candidates are asking for to perpetuate information asymmetry.
[1] https://en.wikipedia.org/wiki/Yao%27s_Millionaires%27_Proble...
Why pay for a service when you can just ask? Basically they do it on purpose because they have the upper hand.
You have very little unique information when you enter the negotiation (you know your current salary, your desired salary, and how badly you need the job—that's about it). They have tons of information that you don't have (what they're willing to pay, what they're already paying others to do the job, how badly they need to fill the position, how badly they want you in particular).
By waiting for them to make an offer, you retain the unique information you have AND you wait for them to reveal some of the information you didn't have. When they make you an offer, you now know approximately what they're willing to pay you to do the job. This is a very big gain for you and allows you to negotiate much more effectively and increase your salary.