The last mile is a solved problem. Most people can walk (and many of those who can't would need human assistance anyway). And then there are bikes, electric scooters, and other light vehicles that use space much more efficiently than a car.
Self-driving cars may help with the actual weakness of transit, which is the long tail of trips. Trips on routes with too few passengers to justify good transit service, and with the trips too long for the last-mile solutions.
Walking a mile with groceries or a baby is common. People in less car-oriented neighborhoods typically do quick visits to a grocery store when it's convenient for them several times a week, rather getting a week's haul of groceries in a single visit.
With furniture, you usually pay for delivery. Especially because the furniture store probably doesn't have the items you bought on site anyway.
When there are grocery stores within easy walking distance, people tend to grab the next few days’ worth of groceries. When everything is inconveniently far apart, people drive forever away to get giant stocks of things from Costco to haul back to their house.
If people aren’t spending $12k a year[1] to own a car, paying $50-150 to have a large piece of furniture delivered isn’t a big deal.
When there is well maintained, pedestrian friendly infrastructure, instead of a tiny uneven sidewalk inches away from 45 mph traffic, pushing your baby stroller home is not an issue.
Self-driving cars may help with the actual weakness of transit, which is the long tail of trips. Trips on routes with too few passengers to justify good transit service, and with the trips too long for the last-mile solutions.