Today, I ran across the above image on Twitter. It made me laugh because it reflects the historical reality of the industrial disparity between the United States and Japan during World War II. The Japanese Empire was doomed because it gravely misunderstood both American culture and the importance of industrial capacity in a war waged in the 1940s.
To my knowledge, the United States did not have a ship dedicated to producing birthday cakes. But it did have a vessel devoted entirely to the mass production of ice cream for sailors. This was a BRL (Barge, Refrigerated, Large) of the US Navy that could manufacture 1,500 gallons of ice cream every day.
Yes, my sources are unclear about whether it's 1,500 gallons per day or or per hour. But at that point of ice cream production, it no longer matters which is correct.
Time-Life - your source - says 1,500 gallons per hour, but those are recent sources. Publications from 1945 say things like "The machine can make 500 gallons of ice cream a day —with storage space for 1500 gallons more." and "a special unit which turns out 10 gallons of ice cream every seven minutes". There is even a picture of one of the 125 hp refrigeration engines .