"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." -- Richard P. Feynman
Your hypothesis doesn't take into account the complexities of people's lives which often overwhelm simple economic models.
1. 26.4% of all US renters spend over 50% their income on rent. The most commonly agreed-upon sustainable percentages are between 25-33%.
2. Sadly, there doesn't appear to be much correlation between the cost of transportation (car purchase, gasoline, car maintenance) and mass transit/car pooling increases. In North America, the idea of status being linked to the automobile is a strong counterincentive to mass transit/car pooling. People would rather be poorer than to be thought as too poor to drive.
3. Switching from one fuel to another is not a simple choice for homeowners, you need to switch your furnace (which may be tied to a long-term contract with the fuel supplier), you need to have a local supplier, and you will inevitably face the fact that as demand in the new fuel increases, so will its price.