Are you navigating by paper map, by cue sheet, or by a GPS device? The GPS does allow you to follow very complicated routes, with lots of turns. This can get you off the main roads and onto quiet country roads.

I've looked at some official state bike routes. (For a few different states. Perhaps some states have awesome routes.) They seem to want to avoid lots of turns, tending to stay on one medium duty road for quite a while.

The Strava Route Builder often makes a complicated route, to stay on popular biking roads. No problem with a GPS showing the route.
See my post about ridewithgps, Strava Heat Map, and Strava Route Builder.