It's a good thing we're not inside the minds of the characters, since those sirens and loud noises would get annoying really fast.
But that's not the only reason Vonnegut chose this perspective. A lot of the fun of analyzing "Harrison Bergeron" comes from trying to figure out just what the characters are thinking. Were they that dull before the handicaps? Why is Hazel crying all the time? And what's going through a fourteen-year-old boy's head when he declares himself Emperor on TV?
Well, we know the answer to that last question: Who doesn't want to rule the world at fourteen?