Traffic might be worse, initially, but once people are okay with sharing seats in a van, you might see a massive rise in ad-hoc ride-sharing/carpooling. These services know where you're getting picked up and where you're going, so there's no reason that can't route close vehicles/riders designating as okay with sharing to have a higher rider ratio per trip. Even with increased total per-person trips, we might be able to achieve a relatively low per-vehicle trip increase.
Couple that with the ability to reclaim a lot of space designated for parking, and forward thinking cities might make themselves much more walkable as well.
Couple that with the ability to reclaim a lot of space designated for parking, and forward thinking cities might make themselves much more walkable as well.