I have never seen anything authoritative as to why the Army wanted to go to .45 caliber rather than to continue use of the .44. Mike's belief that it was just so the rifle and revolver would be the same caliber may be as good an idea as any, even if the ammunition was not interchangeable.
But the desire to go "one up" to .45 had ramifications. Since Colt wanted to use as much of the old percussion revolver tooling as possible, they tried to keep the .45 cylinder diameter as close to the .44 diameter as they could, which resulted in a cartridge case with a small rim. That made no difference in a revolver with an ejector rod, but gave trouble when attempts were made to use the .45 Colt in rifles and the later swing-cylinder revolvers.