>And then consider if you are are the spouse or parent of a murder victim or missing person, and are innocent. You are almost certainly going to be a potential suspect, but you also want to help them find the actual criminal, and if hiring a lawyer makes you "look guilty", then the police might focus their investigation on you rather than finding the real perpetrator.

I agree. This is a real problem in law enforcement. The issue is that while they're competing interests, my right to remain innocent should rationally supersede the deep profound desire for justice (but I recognize it rarely plays out this way).