 The most up to date guidance for classifying US roads is located here: https://wiki.openstreetmap.org/wiki/United_States/2021_Highway_Classification_Guidance, and this page states that "Lower classification [secondary or lower] levels should be applied to roads based on their relative importance to local transportation."

The classification that you mentioned works well in the eastern US or in Europe, but is a terrible fit for the western US due to how much lower density the region is. That's why the western US has been moving away from that, in my experience and from what I know.

So the purpose of these classifications is as follows: trunk roads are the most important routes intothe major towns and cities: my definition for this is approximately >20,000 people. Primary roads serve as links between the mid-sized towns (~2000-20000 people), while secondary roads link the smaller towns and serve the less-important links between larger towns and cities.

This leaves tertiary roads in rural areas to link unincorporated communities or somewhat important destinations (e.g. major parks) to each other, and also to represent roads that could reasonably be used as through roads. Tertiary roads can also be distinguished from lower classification roads by their characteristics: in general they're designed for higher-capacity travel than unclassified or residential roads, often including features like striping or higher speed limits.

Then unclassified for roads that really have no reason to be used for any through traffic that don't serve primarily residential usage (e.g. farming, recreation, logging, etc.), and residential for roads that just serve residential uses.

Does that help answer your question?