I'd say it differently: most people in the US have no safe place to bike for transportation.
Most places are perfectly safe. I for example, have 100 miles of safe trails and rural roads to ride on, here in the American Midwest. But most people live in dense urban environments.
Even in your rural example, those trail routes I find are mostly just scenic rides through parkland rather than anything useful for commuting. People mostly drive their bikes there and ride back to where they parked afterwards. Smaller rural roads might be fine, but I bet you aren't riding along the shoulder of a four lane state highway with a speed limit of 55 miles an hour very often, and those are the main connective roads between job centers and housing among rural and suburban areas in the U.S.
My local town is quite safe and has trails criss-crossing it. But truthfully most Midwestern trails are 'trails-on-rails' and inhabit old railway right-of-ways. Usually pretty far off the beaten path to be sure.
For instance, I can ride 50 miles from my urban center (for what its worth) to the next one north, and be in countryside the whole time.
Most places are perfectly safe. I for example, have 100 miles of safe trails and rural roads to ride on, here in the American Midwest. But most people live in dense urban environments.