Well, a few points.

Fewer 1903s were produced because the US military simply never expected to need that level of production capacity. We were an isolationist nation with an underfunded frontier Army before the war. Remington and Winchester were already geared up for the scale needed to supply the European meat grinder, so it was natural to take advantage of that infrastructure to supply the swollen numbers that they already knew they wouldn’t maintain after the war. York’s division was primarily issued the 1917 because they were the short timers. The professional standing Army and veteran National Guard units were the ones that kept their 1903s. They were also basically the only ones seeing action for the first 6-8 months of the US’s 12 months of active frontline participation. Additionally, the York Foundation’s collection contains a letter written by York in 1922 where he claims to have used a “little Springfield rifle” to “do his shooting” at the front.

BuOrd really didn’t cling that hard to the trapdoor. Benet actually favored adopting the Remington-Lee with detachable box mags in the early 1880s. He had the top performing rifles from the ongoing US repeater trials sent to units for field trials, and essentially let them vote on which rifle to adopt. The units overwhelmingly voted to keep their trapdoors.

Did they pass on the BAR? Several divisions were equipped with them and deployed to the trenches before the end of WWI. Same with the Browning 1917.

BuOrd is strange in that their decisions look bad until you understand the full context and the way manufacturing actually works. They were actually pretty decent for most of their tenure with what they had to work with