No offense but that is fucking dumb.
It is anything but, if you had nothing to do with the disappearance and you want to
help find your loved one then assisting the police in finding them is the most logical thing to do.
Yes, you have a right to a lawyer, and you might even want to lawyer up instantly - especially if they drag you in as a suspect - however the idea that the perception you create in such interviews does not effect how the police view you is naive. There was actually a case in the UK where they were interviewing people for a cold case about something that occurred 20 years ago, the fact one of them started saying "no comment" to all the questions is what made the police focus more attention on them.
If your top priority when your wife/child/best friend goes missing is to protect yourself rather than helping to find them, that is sus. It's not going to have an impact legally, but it will draw attention because it's not normal. If you are able to give them information that rules you out, and you behave how a concerned family member would then you are going to be in a better position.
Just look at JFG, the mother of his child has been missing since June and his response is:
I uhh, was using uhh, myuhh phone and so was she, and uhh I can prove that I could not have been involved uhhh with her disappearance uhh. Instantly, I think this guy is involved. It's not normal behaviour, normal behaviour is to be worried about your fucking spouse.
If you lawyer up, and seem to only care about the legal consequences to you, you are going to draw police attention AND media attention. Look at the Jean Benet Ramsay (fuck all these french names) case. Personally I think the parents did it, but if they didn't... their behaviour with the police - that seems to be primarily based on self-preservation rather than assisting them in finding who murdered their child - has meant they have spent the last 30 years being viewed as probably having murdered their daughter, or covered it up.