Cars are successful because they work in all climes, are enclosed, and don't make people sweaty. Bikes will not work in a lot of places with snow because plowing doesn't really remove ice patches and winds can be brutal (40 - 60 mph gusts). The future replacement for cars will probably use the same infrastructure and be powered and enclosed.
As to the no need for showers, it seems a lot more people who think they don't need to shower actually do. I had a cube two rows down from a biker that believed that, but it wasn't so.
I think cars are successful for more complicated reasons than that, such as the physical and sociopolitical infrastructure invested in them, and advertising and culture. I can't speak for anywhere but the northeast US, but within every metropolitan center over here, biking would be a better form of transportation for at least half of city dwellers, 90% of the time--provided they all woke up and did it at once, regaining road-space from the taxis and the cars. Imagine New York, Toronto, or Boston with one full lane of every avenue bustling with bikes, the way you do in Amsterdam. There simply aren't enough ice patches and 40mph winds in any of those places to justify the level of car traffic. Also, anybody that currently rides the subway/bus/train or walks is already sweating and does not feel entitled to their own enclosed space.
The road to better health is paved with sweaty armpits. I for one would not mind a little workplace B.O. if it meant for happier, safer commutes and fewer billions spent treating the pandemic of heart disease and diabetes. But that's just me.
As to the no need for showers, it seems a lot more people who think they don't need to shower actually do. I had a cube two rows down from a biker that believed that, but it wasn't so.