The decision was based on money. Post-war, no money for the Army. Big time RIFs. Typical post-war cutbacks. Use a modified standrad rifle you already have, or buy new ones? In that economy, you go with the cheap solution.
Also realize that there was a huge bias against a high-firepower, small caliber shorter range shoulder weapon. Sound familiar? The Trapdoor was a "real" rifle, in a "real" rifle cartridge. The Henry was a "mouse-gun". That type of bias runs deep in the military against trying new things and abandoning the old ways. Then as it was today. The same arguments used against the M-16 were used against the repeater: Troops won't aim, troops will use too much ammo, troops won't be able to engage targets at 2000yds, etc. Combined with the cost of new rifles and the repeater didn't have a chance as a general issue weapon.
In the end the Trapdoor was cheap, worked, and was fast enough for use in the west. There were better weapons to be sure, but the outcome wouldn't be dramatically different.
Ross