The problem is that the investigation is about figuring out who is actually the criminal. Cops deal with mostly bad people. Actually innocent people who get caught up in the criminal justice system are relatively rare -- ask any defense lawyer. This makes investigators incredibly jaded and willing to treat everyone as guilty because it's usually right (and even if they didn't do it they did something).

This is what makes your take on this question so dangerous. This is not about how cops are allowed to treat people they know are criminals, this is about how the cops are allowed to figure out if someone is a criminal in the first place. Telling an innocent person "we have DNA and video of you committing the crime, just plea down to manslaughter and you'll be out of prison by the time your kid graduates highschool" puts them in a devastating position. They may decide that they've been framed and just confess because they think they either do it today or face mandatory life without parole. Even if the majority of people put in this position actually did the crime it's still wrong. Same goes for beating confessions out of people.