> mostly be glad to use driverless cars,

Exactly!

a) As it says in OP's text, the most dangerous point in driving these automated cars is when a half-distracted driver takes over; having a fully automated car prevents this.

b) OP's text seems to see the biggest danger in automated cars not reacting properly to other humans driving erratically. This is easy to fix - once 100% of a road's cars are automated (and ideally communicate with each other), the problem of erratic driving simply disappears.

A question for thought: If I'm drunk in a driverless car, current laws would say that's illegal, since I'm still the main driver. But if it's fully automated, why should I stay sober?