The military needs more firepower.
..and able to reload that firepower in a hurry.
Seriously, the revolver had been the stable of American law enforcement since the Civil War - even before in some areas. It was classic Americana. Too, by the late 1800s, even the military was downsizing in caliber - by the Spanish-American War, the Army had gone from .45 down to .38. As eastern jurisdictions were looking for guns for their constabulary, the .38 was a natural choice - even the army was using it! - and revolvers were a known entity. Colt, Smith, et. al., were the cream de la cream and cops armed with these guns were sufficiently loaded.
But, in the S-A War, it was discovered that the .38 slug was insufficient for the purpose. It was a poor manstopper. The Army rushed old .45 Colt revolvers through rehab and started sending the old thumbbusters to the battle lines.
As the military was upgrading to the automatic pistol and Browning packaged the .45ACP and 1911 together (skipping the history of the 1903 Colt, etc.), the military decided the power of the .45, plus the quick reloading characteristics of the automatic, plus the relative ease of servicing the 1911 all made it a wise decision.
Many western law enforcement agencies - including the Texas Rangers - adopted the 1911 after WWII, partly out of plenty of guns being available, partly because they worked well, especially for officers where backup might be MILES away. But in New York City, heavy firepower wasn't needed. The .38 Special was sufficient unto the day thereof.
Many agencies liked the revolver because it was a relatively easy tool to be trained on. A bucket of .38 wadcutters was a lot cheaper than .45ACP. A revolver's gentle roll was easier to handle than the 1911's rattling and sliding around in the hand. A .45ACP has almost 2x the felt recoil compared to a Smith M&P/model 10. For officers not used to "big guns" - both size and recoil - and civilians not used to seeing cops with cocked (and locked) guns, it was too much. Politics were a big part of government life back then, too!
Q