and we wouldn't have to worry about being late so much because of traffic jams
I'd expect there to be far more traffic jams because no longer is there an incentive not to let your car drive into the city.
Can't find a parking space - just leave your car driving around. Intelligent cars would actually seek out traffic jams so as to minimize fuel use.
Almost at your destination and crawling along. Get out and walk the last bit and let your car get there in its own time.
Stuck in traffic jam, get out, pop to the newsagent catch up with the car and get back in again.
For the more proactive, stick your Brompton in the back and let the car drive most of the way to the city. Once it starts getting snarled up in traffic, hop out, cycle the rest of the way and let the car do the rest of the journey on its own ready for when you want to leave.
Time it right, and the car will arrive just as you're ready to load your shopping (and bike) back into the car. Hopefully, these automatic cars won't block the roads for the drivers trying to leave the city so the route out will be fast, unlike human drivers who block junctions all the time.