"This man's voice is very loud."
Although grammatically correct it would change the nuance, specifically pointing out that a particular man in the room was loud, compared to the others. Speaker 1: "There's a guy in here with a really loud voice, who is it?" Speaker 2, pointing: "THIS guy has a loud voice".
I found this page helpful http://nihonshock.com/2010/02/particles-the-difference-between-wa-and-ga/
The word "This" in this sentence calls to mind a scenario in which I'm introducing a man, whose name I do not know, to a friend, because I'm impressed with the volume of his voice.
Me: "Check out how loud this guy's voice is!" This Man: "AHHHHHHHHHHHHHHHHH!!!!!" My Friend: "...neat."