In cities where public transportation is a huge success, it's because driving is completely impractical due to congestion.
Even a first class compartment on a train is frankly uncomfortable compared to sitting in a car.
An autonomous car or a chauffeured car beats it hands down, because public infrastructure is never going to be as clean or as luxurious as an individual can afford.
I love public transport and I want it to do well because, well, it's ultimately the only thing that's going to scale. But it's just not acceptable to say "oh well the train is warm and smelly, deal with it". Unless it's a cause that really matters to them, most people who can afford it are going to opt out of that.