It's not "having a lot of money". It's actually "having a lot of options".
By definition, rich people will have more ways to get around than poor people. The rich can hire a limo, hop in a helicopter, and even take a trip to space.
Is it a social injustice that not everyone can afford a limo, helicopter, or spaceship?
I do not think it's bad to take steps to make driving an activity for richer people, to make it a luxury that it initially was when cars were invented.
On the flip side of things, look at what the dream of mass-market affordable cars, free highways, and free parking have done to society: Swathes of land wasted for parking, low density cities that kill walking/cycling/transit, millions of people dying in car crashes, endless congestion and lane-widening.