I suspect that many of the accidents that happen with touchscreens are frontal collisions with slowed down cars when the driver is distracted with the touchscreen. A few regulations that might help with this:

All cars with touchscreens need to have automatic forward collision detection and emergency braking, and if it's not enabled, the touch screen should have very limited functionality. No scrolling music, no sending texts, etc.

A car with forward collision detection should show a clear warning a few seconds before it triggers the brakes, and indicate the warning on the screen. Chevy is already doing this by showing a "seconds before collision" indicator on the display in front of the driver. They should make it even louder (visually) and disable the touchscreen if it falls below 2 seconds.