In this case, I would guess there were family concerns over enlistment. Wash was the oldest child; he and his father were the only men over 15 caring for his 7 sibs and 3 young aunts/uncles in the adjacent household. I've tracked the older paternal uncles and they were Union. The bio revealed Wash's mother was a Scott, descended from Samuel Scott, pro-slaver hung in Kansas prior to war.
As part of this project, I've been through Bates County probate files for the 1850s - 60s. Wash's father administered Scott estates--Wash's maternal uncles according to online genealogy sources. One of them matched a CSA who died in Union custody of illness. I don't know the cause of death of the other. Presumably, the other was also a defender of southern cause.
It might have been hard for Wash to join a Yankee outfit given his mother's sensibility and family circumstances. I didn't find Wash in the consolidated draft list, so presumably the local officials knew what he was doing. The list included several young men who were marked "gone to bush."
The explanation you offer fits his circumstances, has precedent, and matches his bio. All of the Harvey uncles went to Cavalry units and Wash went on to be a teamster in California. Likely, Wash was a good horseman.
Now I can move on to the next household in Pleasant Gap. You've given me a great gift with the names of the various regiments that might have picked up a Bates County person. Thank-you so much for elaborating on which units you checked.
--Jean Dresden