Price anchoring is a pretty well researched/understood phenomenon though - as in, whoever comes up with the first number sets the tone for what's "acceptable". Someone who negotiates down from that number feels like they got a better deal than someone who was negotiated up to it.

I admit it's not exactly applicable to salary negotiation, but IMO leading with a high number can help cement the counterparty's perception of your value. I think it really depends on what type of company (and what level of its food chain) you're applying for.