This is probably about recognizing (legal) rights, and eliminating reasons for prosecutors to breach rights. Much of the Anglo-American criminal law is about being fair to defendants - only convicting when the proper standard of proof is met by the proper means.

An alternative approach would be to allow such evidence at trial, and severely punish investigators who breach rights. This would avoid some technical acquittals where the evidence supports conviction. However, a reluctance to punish high-status investigators means this approach could just result in more breaches of rights.

IIRC, the reason the exclusionary rule came about in the first place was because the previous system of suing police officers who introduced improper evidence didn't work - it's hard to do that when you're imprisoned, and, as billswift pointed out, juries are reluctant to rule against police. In order to make this work you'd need much larger changes to the system to go along with it.