You can cycle many miles of interstate highways. You can expect many multiples of punctures in your tubes. They are punctured by radial wires. You will suffer far fewer flats on the mapped bicycle routes.
Mapped routes could ensnare you in the convenience-store trap. Multiple dinky little towns where cafes are closed, where only health-altering junk foods are available are irresistable to energy-hungry bicycle tourists. Going your way gives freedom to chart a course where real nutrition is available
Using unknown roads could get you into a jam, e.g., extreme noise, pollution, fast and furious insane traffic, grueling long climbs, crumbling deteriorated road-surfaces, unanticipated complications. The ACA mapped routes are very well known. Those problems are solved for you before you spin your first revolution.
Using mapped bike routes, you are just another cyclist passing through. Same old, different day. Adventuring your way could take you to places where cyclists never travel, and here you are the talk-of-the-town. I cycled through a foreign country that showed on television secretly-recorded videos of me cycling there. I have no idea how they got those pictures. I had no idea until I cycled into these villages. People approached me in the streets. "American, American. You are on TV television."
Five times for me from Florida to California. Twice from FL to El Paso, Texas. Mostly I free-camped. Quite a few motels. Van Horn was my favorite. Used designated campgrounds only a few times. I took many routes not on the ACA maps. I took many that are on the maps. On a broad scale of equalities, I say using the mapped routes is the best way to go. But not always because of variables.