The American army really had no chance of defending New York, being outnumbered, undertrained, and without a navy. What if Washington simply abandoned the city, as he claimed he wanted to do, but not allowed to due to political pressure, and took up position in the Hudson Highlands that he would fortify and make almost unattackable later on in the war?
Would this help the American cause long term? Washington would not lose the men he did in the fights for New York, nor would he lose the vastly larger amount of men who simply marched home out of camp during the standoff period at Harlem Heights, nor would he lose the vast amount of men lost in the defense of Fort Washington and the near disentegration of the southern column (most of the army's troops from the Mid Atlantic colonies) in the aftermath of the loss of Fort Lee. But on the flip side, abandoning New York without a fight would not help gain support for the war effort, nor would burning the city, which would make sense militarily but not politically.
Essentially, do you think Washington having 10-15K troops entrenched and unscathed around New York City on the high ground north and keeping the vast amounts of war materiel lost in OTL's retreat from the city is worth the propaganda defeat of abandoning the city?