Yes, evidence obtained through unconstitutional, but honest means should be admissible in court, because there is no incentive to law enforcement in banning the evidence. If information is gained honestly, law enforcement does not need to be taught a lesson about following rules next time, because the mistake was not one of poor intent. The information can come in without rewarding law enforcement for bad behavior.
Too many cases against criminals are lost because the kind of evidence presented is not enough or not admissible due to the way in which it was obtained. We need to remember that evidence is evidence. No, it can not be obtained in devious ways because rights need to be predicted, but criteria need not to be so stringent.