Nostromo provided a pretty good list of reasons why people choose to drive. People think it is more comfortable, convenient, safe, and practical than the alternatives (and it's a status thing for many).
You provided some reasons why you cycle. You included showers and safe bike parking in your list. Those are deciding factors for some people. I didn't mean to suggest they were the main factors.
Most people seem to agree the main reasons why people don't cycle (even when they have a bike and fitness to burn) is the volume and speed of peak hour traffic - it's unpleasant and possibly dangerous. That's the big thing that has changed over the last 20 years.
What to do? In the UK there is a 5-step Hierarchy of Treatments used by city planners trying to design for cycling.
1 - Reduce Traffic Volumes
2 - Reduce Traffic Speed
3 - Traffic Management
4 - Reallocation of space (e.g: bike lanes)
5 - Specific Cycle facilities
Mayor Ken Livingston has shown how effective the first 3 measures can be. You might argue he forced his measures on the public and that is a bad thing. But it's no different to forcing people to give up smoking. Nearly everybody is better off for it, and in the long run people thank you for it.
The libertarian approach of giving people what they want
The Dutch are even more successful - their CROW guidelines list the following requirements for cycling routes:
1 - Coherence
2 - Directness
3 - Attractiveness
4 - Safety
5 - Comfort
The libertarian approach of giving people what they want should be a part of the solution, but in that regard, the easy gains are to be made by getting recreational cyclists out of their cars (ie: by providing for all cycling needs, even showers).
As far as the majority of drivers go, a mix of carrot and stick is required - better public transport and pedestrian facilities AND less parking, lower speed limits and taxes that cover all the costs of driving (roading, health, and environment).


















