I don't have a self-driving car (of course) but I do have recent one with several automated systems.
For example the rear parking sensor - it's OK-ish, but so paranoid that I wish it would STFU when reversing into a parking space of less than (say) 12 yards long.
For example the windscreen wipers - they're OK-ish, they run when it rains, they don't when it doesn't, but seem really undecided about drizzle. Not had the chance to check them in snow yet, but can't say I'm optimistic.
For example the lane-departure detection system - it's OK-ish, but it can't detect white lines if they're not recently painted, or if there are those shiny strips of tarmac that are sometimes used to form the joins around surface repairs. It's supposed not to worry about lane-departure if you signal beforehand, but evidently disagrees with me as to the meaning of "beforehand". It signals lane departure by vibrating the steering wheel, which is of course undetectable when driving on a typical British road surface.
And so it goes - the more complex the system, the less useful benefit it gives, and the less able it is to cope with real environments. So colour me sceptical about linking lots of these bits together into a more complex system.
BTW, the paranoia point is especially significant, I think. Automated vehicles will simply log-jam our roads because their programming will make them too cautious, I expect. And don't say the onboard "AI" will learn when it's safe to go faster, because that feature will definitely be locked out.
I may be biased, I enjoy driving after all. Maybe we should make it a requirement that self-driving cars also provably enjoy driving?