The exclusionary rule is there to protect the defendant, and the defendant can ignore/waive its application.

Even if it could be applied without regard to whether the defendant objected, it has been gutted in recent decades by our radical right-wing Supreme Court, who think illegally-obtained evidence is just dandy so long as excluding it from court proceedings wouldn't actually change the government's behavior in collecting it.

My understanding is that such evidence is only thrown out of court when challenged by opposing counsel. For example, a prosecutor puts forth some evidence, then the defence lawyer objects, and the judge rules on if it is admissible. If the defence doesn't object...

That requires admission of illegality

I don't know why but this put this all in a whole extra sharp perspective for me.