Short Pump and Tuchkahoe are just census-designated places and do not have their own governments. Tuckahoe is a magisterial district of Henrico County but it has no individual government. While I understand it appears to be a loop, on the southside of the James river, there are interchanges with VA 150. Once VA 150 ends and becomes VA 37, it no longer has these interchanges as it going through neighborhoods. Looking at streetview level images of the two roads can clearly show why Parham should be primary and Chippenham is a trunk/motorway. As a local of the area, I know this for a fact. Looking at the trunk roads in the RVA area, they all appear to have been upgraded to trunk roads by yourself.