Lately, I have noticed that many people who wear a tallis during davening will deliberately put on the black hat, which they wore on the way to shul, while still wearing their tallis near the end of the chazzan's recitation of mussaf. I have observed people going well out of their way to the coatroom just to get their hat for this when they easily could have gotten their hat as they were leaving shul.

Is there any explanation for this practice? Wouldn't it make more sense for them to put on their hats after taking off their tallis?