Do you (cops) prefer to carry your handcuffs exposed to view or in a pouch and why?

Sounds like you may have spotted a "handcuff strap". There are all kinds of options for carrying handcuffs these days, all kinds of cases, pouches and straps are available. Some are open some closed. How an officer will carry their tools will depend a little on personal choice and a lot on what the department issues. Personally I've always preferred a closed case. A closed case helps to keep the dust and dirt off them and in my opinion looks more professional. I agree with your "in your face" quote. I personally think the look of the "Boston leather handcuff strap" is quite sloppy. But that's just my two cents.