Every day drivers operate far more complex vehicles than a car. They can drive and steer, eat a snack, drink coffee, smoke a cigarette, shift through 8-10 gears, get info talking on a radio or phone, monitor a large cluster of gages, even write down fast information like state line mileage off their odometer and have done so safely for decades. They are truckers.
If you can't talk on a phone hands free and drive at the same time safely then by all means get off the road because you likely are a poor driver under any circumstances. For such drivers removal of cell phone will not improve their driving skills. They have poor driving skills too start with. That is the real problem. Not the phone usage.
As far as old cars being safer, that's only by way of their being heavier. Some new roller skate cars are ridiculous. I looked under a Saturn on a grease rack once and decided never to get in one. The rear undercarriage was more flimsy that the coaster wagon I had as a kid, the tiny rear axle “supported” by 3/8” steel rods. However, new cars are designed to protect the passengers, not the car, and the car self-destructs around the passenger compartment. The car is totaled but the passenger space (usually) remains intact. Look at some old accident photos from the 30’s, 40’s, and ‘50’s. Those ‘40 Fords remained largely intact, but the people inside were reduced to hamburger from being slammed around in a steel cage full of broken glass. Anyway, I drive an extended cab 4x4 Chevy Silverado with airbags and seatbelts (and only carry a cell phone to make emergency calls), so when some kid plows into me while yakking with her friends, I'll probably be OK.