The key to this implementing this sort of policy without hurting poor people is to introduce a corresponding tax credit or stimulus payment (potentially means tested) such that driving a normal vehicle a normal amount comes out even and poor people can actually come out ahead if they make more responsible choices. You want people to feel it at the pump so it affects their decision making without having it be punitive.
Sounds like it’d hurt poor people unless they make what you call more responsible choices. A difficult part about being poor is you often don’t have as many options. There is a lot of reasons why that turns up, but it’s there all the same.
The ability to buy a car with a loan is very widespread. It's easier than cash if you're poor, isn't it? And with a loan you can balance vehicle cost against gas cost easily.
The key to an inefficient government is taking money and redistributing it.
How much does it cost to execute this whole plan? You end up taking a large percentage just to run the program with little to show for. It does make for great political campaigns.