not in my lifetime

Not widespread and not in our lifetimes.

Autonomous vehicles are a possibility,

Tesla FSD is still full of issues, but with super fast 5G and better infrastructure-car communication it can solve lots of issues.

But I really don't see cars with no steering wheel becoming mainstream in the near future, maybe in 25-50 years.

Where I live "public-shared" cars are already a thing, it's called AutoTel and it is even somewhat popular.

BUT, With such cars, they have to be new, maintained, fully insured, always fulled SO they end up being super expensive!

The AutoTel costs something like 40 cents a minute in town and 90 cents a minute out side of the big city...

And all of that for the pleasure of driving a publicly owned Hyundai i10 city car

(for reference, my 1 hour commute, in my small Crossover SUV, costs me $17~$18 including fuel ($4.5~$6.0), including maintenance (~$1.2), and including the unreasonable cost of buying a new car where I live assuming even a lifetime of 10 years which equates to about 90k miles (~$11) -

MUCH cheaper than a public stinking i10, as a matter of fact, over 3 times cheaper and no need to worry about a car not being available during rush-hour)

On a less serious note,

There are already electric public vehicles that you do in and they drive you places without need to drive them by yourself.

Fully autonomous driving won't be happening now. Replacing private ownership of a car with this is an absolute NO.

Autonomous vehicle is not going to happen at a widespread level. No matter how well trained a software and AI system is, it's still a system designed and programmed by human beings and it can't think like humans can. Something like this can't be mixed in a place with cars being driven by humans, bicycles, pedestrians, etc. because so much can happen that we as a human can think and decide how to react at the moment, but a software can't do that. We will be seeing private ownership of cars for many many more years.

In select big city with high and dense population, with limited parking. Possibly. 

In most of America, most likely not. We’re probably one of the least dense industrial nations overall. 

I suppose it depends on how many people are prepared to see others die when the car gets the blue screen of death and crashes.

I'd say no, but maybe if we allow 20-40 years of brainwashing, several generations from now will look back at us steering cars like I watch a tightrope artist walking between two high-rise buildings. And they'll get a caveman look of awe and confusion on their faces for a brief second before their attention shifts to other things in their virtual worlds.

While the rich are being chauffeured around in their V12 combustion engines. 😉