I personally believe once we go fully autonomous in the automotive industry and people are accustomed to trusting AI with they're lives to transport them in cars it will change the perspective of the public. (not saying that automotive AI and aviation AI are at all same level of complexity, but I do think public opinion will change)
People can't drive worth crap. Most non-alcohol accidents involve distractions, inattentiveness, carelessness, and/or aggressive/reckless actions. Throw in some for weather, but again, a slower/cautious speed would do wonders to reduce those accidents too. An autopilot car doesn't have the complexity of the human mind, so it won't be distracted or do stupid things that humans tend to do all the time that cause crashes. If pilots flew like how the average person drives, there'd be a lot more dead people. Thankfully that's not the case, and aviation today in America is safer than ever before.