More than anything Crozier may or may not have done, I think the real issue in acquiring/developing weapons for the US Army in the years just prior to entering WWI was "politics" and geo-strategic interests.
Politics: The US simply wasn't expecting to be involved a foreign war - especially those in Congress. In 1914, President Wilson was preaching "neutrality." The general population embraced this idea; there was no interest in getting entangled in Europe's problems. Even when Germany pushed submarine warfare, Wilson desperately tried to avoid getting involved. Of course, we'll see that by 1917, there was not much choice left.
Of course, none of the political argument above means the Army shouldn't have prepared; after all, as Sun Tzu advised, "In Peace, Prepare for War." And MG Leonard Wood agreed; however, Congress wasn't appropriating money. And what money the military did get...went to defending the Philippines, Hawaii, Panama Canal Zone, and Porto Rico. Today's "shift to Asia and the Pacific" away from Europe in US security policy isn't anything new. And let's not forget that Mahan's book, The Influence of Sea Power upon History, influenced US geo-strategic thinking as well as fueling the naval arms race in Europe. And to the US, that meant the Pacific. Many of Crozier's disappearing carriage guns were in coastal defenses in the Philippines and Hawaii and the West Coast of the US. This is about the same time the US Coast Artillery was gaining prominence. As a result of the Spanish-American War, President Theodore Roosevelt (former Assistant Secretary of the Navy during the war) and Secretary of War Taft presided over splitting the Coast Artillery from the Field Artillery in 1907; Congress authorized expanding the new Coast Artillery Corps to 170 companies and legislated money to build coastal defenses across the US coast and territories (called the "Taft system of fortifications"). Unlike the Field Artillery, the US certainly had a Coast Artillery Corps and coastal defenses to equal any nation by the start of WWI. Because it received funding to respond to geo-strategic priorities.
Needs of the Army Published: January 19, 1914 Copyright © The New York Times
US political and geo-strategic focus was not on a land war; thus the need for machine guns and field artillery didn't make it into the budget priorities... Even if Crozier did want the Lewis gun, there wasn't a "need" nor "interest" - therefore, no "money."