As an American, I find the concept of throwing out evidence somewhat questionable is well, as in, if someone is guilty, they are guilty, no matter how the evidence was obtained.
Don't worry, you're not the only one. There was a study that found that 70% of juries still convicted based on the very hint of thrown out confessions (when no other evidence was present to corroborate the guilt of the accused).
This has lead police officers to purposefully avoid mirandizing some of the suspects they arrest, and then interpret almost anything they say as a confession (while at the same time making sure that any recording of the so-called confession gets conveniently lost). Because once the district attorney mentions that there was a confession in front of a jury, and even if the judge throws it out, the accused is then caught in a bind, either he says it wasn't a confession and that claim (that he confessed) possibly gets used against him officially (because as a defendant, if he brings it up in court, it becomes admissible), or he says nothing and the so-called "confession" still possibly gets used unofficially against him by the jury.
This is why you should never talk without your lawyer present. Your lawyer should always bring in his own recorder as well. And you should never answer hypothetical questions about where you think a potential murderer could have buried the body, or what was possibly used to commit the crime, or really say anything at all, until you speak to your own lawyer first.
The truth is that the real harden criminals and the real psycopaths do not confess. They just don't. And that the US criminal justice system makes it so damn hard to convict any kind of people without direct evidence, that we've given the police and the justice system an almost impossible job to do. That's why extraordinary measures are being taken on an almost daily basis to try to make the system work (despite all the rules that prevent it from working in the first place).