Your claim is that P(consent | sexy clothes) = P(consent | not sexy clothes)? Seems counterintuitive. Do you have evidence to support this claim?

If the prosecution, in anticipation of defense strategy, believes that what a person is wearing, among a collection of facts, may be utilized by defense, then of course it's to prosecution advantage to have the police ask first on their terms, as opposed to letting the defense ask these questions on their terms. That way the police and prosecution can control the progression of fact discovery.

It's because prosecutors understand factors to legal victory that clothing, drug use, prior relationship with defendant, and other things like that are relevant.

Speaking descriptively, the job of the police is not to act as some neutral 3rd party of justice and investigate all claims of the truth in proportion to their merit. It is the secondary job of the police to set up cases for the prosecution without regard for defense interests. It is the primary job of all agencies ever to manage organizational credibility, robustness, and scope.