In my view, the criminal trial should be all about a reliable determination of whether the defendant did it. All reliable evidence should be considered. If you want to put the police on trial for what they did, that should be a separate case.
One of the objections to eliminating the Fourth Amendment exclusionary rule and relying on civil remedies is that the doctrine of qualified immunity prevents the resolution of previously undetermined questions. That is, if the searchee sues the police officer, the officer is entitled to immunity as long as what he did was not clearly illegal at the time of the search. So how can you ever get to a judicial determination to make the law clear for future cases?
One answer is that if the action in question is a regular practice of the police department, you sue the city, not the cop, and there is no immunity. Today's decision of the U.S. Court of Appeals for the Ninth Circuit in Lowry v. City of San Diego, No. 13-56141, illustrates the point.