Mind reading isn't admissible as evidence, so knowing who isn't the same thing as having the evidence for a conviction. It could be like Columbo, where he knew who did it, but had to prove it.
But that's not the point. The appeal of mystery/detective stories isn't in whether a conviction is attainable; in fact, many mystery stories end without a courtroom-level burden of proof being met. Mysteries are stories about solving puzzles, about using observation and clever deduction to uncover the truth. The detective's victory lies in figuring out the killer's identity, solving the puzzle. That's the climax of the story. Even in Columbo
, the audience knew the answer in advance, but Columbo himself still needed to investigate, observe, and deduce. He didn't "know" who did it, he just suspected, and had to find the evidence to confirm his suspicions. Sometimes he didn't suspect the real culprit until nearly the end of the story. So it was still about the detective using his wits and skill to deduce the answer. Just magically sensing the answer would be cheating.