Yes, when bicycling in my town in Southern California, I often avoid the marked bicycle routes in favor of less busy streets with no marked bicycle route.

That's sad. Though Slovakia is not much better, we do have some bright spots. This is the Eurovelo along the Danube: https://maps.app.goo.gl/yL3Picyo2ZTuDaZ3A

How much traffic can you expect on that road? I rode on similar roads and it was actually quite nice.