An early draft copy of the Machine Cancel Society's listing of "United States Slogan Cancels, 1899-1940", lists this 4-star dial paired with the airmail slogan from Feb 6, 1929 to May 10, 1930.
I agree with Paperhistory, that stars in dials typically represent temporary, replacement-for-maintenance, or experimental uses - philatelic mail would be such a typical case. One of the challenges in large post offices is finding a way to identify the machines (like those needing ink, feed adjustments, date/time correcting, etc). Often this was accomplished by a number in the killer bars. This doesn't work as well when generic slogans are used - like the airmail slogan. Numbering the dials is a nice solution. The stars serve the same purpose - they permitted the rapid identification of a specific machine.
While the stars can be seen as decorative today, I disagree with the theory that the stars are for added strength or symmetry. Countless symmetric dials from short town names exist, which have no extra graphic elements. The steel dials rotate on a shaft and roll against an ink-saturated inking cylinder made of felt and then against the paper mail pieces moved along by rubber-faced rollers. The canceling dies don't touch anything hard to create damage or much wear to steel. Many dials are used for decades.
Here are two other star-dials from New York City on non-philatelic mail, which may indicate use as a temporary replacement machine while one is off for repair (just a guess):