I'm also a daily user of public transport in a major world city, however, and whilst buses and trains work they also have the fundamental problems highlighted above that are in my view insurmountable, and which (self driving) cars solve. So I'm in a dilemma over whether I think they'd be an improvement, but I ultimately believe they would be.
But yes, absolutely pollution and space saving would have to be addressed. I'm optimistic they could be:
Pollution: hopefully solvable with electric. Yes, of course, there are efficiency gains that trains/buses would perhaps always have (having to move many small things rather than one big thing carrying the same number of people) but I can see electric reducing the absolute level of pollution from cars to a point where it basically doesn't matter. Maybe overly optimistic, but I hope that'll happen.
Space: Driverless cars, particularly electric driverless cars, can be much smaller and can drive much closer together. Different cities have different challenges, but I don't see why we couldn't get to a situation where roads might effectively have capacity for 2x vehicles across and 2-3x vehicles along if the vehicles can be coordinated to drive closer together and are physically smaller (remember that on-demand unlocks certain design constraints - you don't have to provision for peak - if the average number of passengers is 1.5, then most cars on the road could be ultra small 2 seaters). Again lots of conjecture and optimism here, and I am probably assuming that 'manual' cars would eventually disappear or be banned at least from cities too, but nonetheless I think there is hope here.