We’ve added digital side bands to “FM” broadcast radio. We’ve fully replaced analog broadcast TV with digital. We can solve this problem, with proper planning.
Develop a digital modulation that captures human voice and degrades gracefully, fund the development of ICs to demodulate it, require AM stations to install a new modulation equipment, and gradually migrating all stations to a hybrid mode with both analog and digital transmission. All new cars must use the new version, which is far more resilient to interference. In 50 years you get to turn the analog transmissions off.
Being able to pick up a station with virtually any radio ever built, or even a simple circuit you can build from spare parts in your house [1]...even if you're on the fringe edge of reception (though it might not sound great) is entire point of AM. You would be throwing all of that away.
Develop a digital modulation that captures human voice and degrades gracefully, fund the development of ICs to demodulate it, require AM stations to install a new modulation equipment, and gradually migrating all stations to a hybrid mode with both analog and digital transmission. All new cars must use the new version, which is far more resilient to interference. In 50 years you get to turn the analog transmissions off.