This made me do some research into "hearsay" because I'm not really familiar with how it all works.
> Per Federal Rule of Evidence 801(d)(2)(a), a statement made by a defendant is admissible as evidence only if it is inculpatory; exculpatory statements made to an investigator are hearsay and therefore may not be admitted as evidence in court, unless the defendant testifies.
So it's not hearsay if it makes you look bad (but it is if it makes you look good), and police don't even have to be telling the truth, nor do they really have to be worried about perjury charges if a given encounter was not recorded.
I still can't imagine why a confession given in interview isn't logically nullified by:
On top of that, statistically, a guilty confession results in a massive bias from the jury, often to the point of completely overriding exculpatory evidence (like, say, witness testimonies of alibi, or forensics).