Most of the biggest safety features that had the most impact were developed in the 1960's and 70's after people like Ralph Nader really pushed the auto industry to do better. There was a second big bump in safety in the late 80's and earlier 90's with the addition of airbags.

I'm pretty sure you could design a car with few or no computers in it that would be on par with most cars on the road today in terms of safety. Sure, you'd lose some safety features like backup cams, but nothing that huge compared with earlier safety improvements.