Motorists would have significantly reduced fatalities if they wore motorcycle helmets (which are much more effective but impractical for bicycles), like race car drivers do, but they don't.
Not quite. In addition to a crash helmet, you would also need a HANS (head and neck support) system, six-point seat belt, a net along the window like you see in NASCAR, and a roll cage. And since it would take you longer to exit the car, you would also need an automatic fire suppression system. At that point it's quite a lot more impractical and expensive compared to a normal car than the difference of bike helmet vs. no bike helmet.
Also, you can get full helmets for bicycling. It's standard issue for downhill cycling, see e.g. here. That manufacturer (POC) have been making state-of-the-art crash helmets for skiing (used by many athletes in the Alpine World Cup) and biking for about 10 years now, so I suspect they've got a much better idea of how to do it than some random guy who tried to improve over $10 styrofoam helmets.