Yes, capitalism is the root problem. Some people argue that you cannot overcome climate change under capitalism (and neoliberalism, specifically).
But I think it’s unlikely we’ll be able to change the underlying system without society collapsing in some way. Or a revolution.
However, I don’t think you have to get rid of capitalism to reduce cars and make a positive impact. Climate change is a scale: the more we do now, the less bad it will be in the future. So doing something is still better than nothing, even if it doesn’t solve the problem entirely.
Reducing cars (and therefore emissions) can be helped by improving public transport and increasing the number of options for transport. In many places, cars are the only way to get anywhere, especially in countries that focus on car infrastructure. Having the options to bus, train, bike, walk, or drive will reduce the number of drivers. In the case of bike lanes, at least in my country, there is evidence that adding bike lanes increases the number of cyclists (and therefore decreases the number of cars on the road). “Build it and they will come,” if you will.
I have a car, but I most often bike or take the bus. We can’t get rid of cars entirely; there are reasons people need them (tradies needing vans with their equipment, certain disabilities needing customized transport options, courier parcel delivery, etc.). But reducing the number on the road at any time is helpful.
Masimatutu