Above is 22 second scene in question.
Thomas and William Bowler invented the Bowler hat in 1849 in London. But why is Jack Benny wearing one in 'It's a Mad, Mad, Mad, Mad World'? Director Stanley Kramer wanted Stan Laurel (Laurel & Hardy) to have the cameo in the desert. He filmed the scene on location with a double who stops his car in the background and asks, "Having any trouble?"
The loud and pushy Ethel Merman yells back, "Yes, and we don't need any help from you." I guess that Kramer planned to have Stan Laurel in his trademark bowler hat do his trademark whimpering. But Laurel decided to keep his promise to never appear in a movie without his lifetime partner Oliver Hardy who had passed on.
So Kramer got Jack Benny to do the studio close-up and give his trademark, "Well," in response to Merman's yelling. Since the location shot was already filmed with a Bowler hat, Benny had to wear it.
***************************
Please check out my movie Forbidden Power on Amazon: https://amzn.to/2nszuEJ