If this 1882 Postal Guide is an indication, not all the letters were needed/used for stations (not branches!) and some were skipped:
Same from the 1887 Postal Guide:
The 1907 Postal Guide listed an explosion of numbered stations running nearly 2 pages up to Station 222.
It becomes clear that much incoming mail was marked as received at the main PO, and then again at the local stations.
The size of New York City makes it a special case. New York City (and in a few other large cities like Boston, Chicago, Philadelphia, etc) made many of their own forms rather than using the normal nationally-distributed forms. This one has a marking with a "NY / 13" in it:
Good luck finding printed regulations or instructions for how New York City handled their mail beyond the general way most cities operated. New York City is such a unique case due to its size that no doubt internal mail handling procedures had to adapt to respond to the volume, transportation logistics, etc.
That said, Marshall Cushing's 1893 volume "The Story of Our Post Office" does have some detail of mail operations in larger post offices including New York City on page 710 and following.
Another very useful book on large-city mail is Leonard Piszkiewicz's epic "Chicago Postal Markings and Postal History".