The legal status of a populated places should not matter when it comes to linking them to the trunk network. Arlington, for example, is a census-designated place, however it is tagged as a city and is linked to the trunk network with highways like US 1 and US 50. It's mainly all about population, and collectively, the Bon Air-Tuckahoe-Short Pump area has somewhere about ~100k residents.

For the US, the popular idea that trunk classification should only be applied to limited-access highways isn't really relevant anymore as it's been shifted to major highways and roads that connect significant populated areas and major transport hubs like airports and seaports. This has been documented in various OSM Wiki pages for most states, including Virginia, which was created by me with feedback from other people during the creation process:

https://wiki.openstreetmap.org/wiki/Virginia/Highway_classification

A couple corrections though, VA 37 is all the way up in Winchester, and Parham is unsigned minus the section between US 1 and 95 where it is VA 73. And a lot of the highways that are classified as trunk in Richmond were trunk before I touched them if I recall correctly, such as US 60 between VA 288 and VA 150 and US 360 west of VA 150 as well as northeast from I 64.