Actually, roads and parking garage and driveways take up spaces that could be used for parks and greenery. You could have tramways with grassy cover, for example.
Every time when I drive to anywhere, I am surrounded by five lane stroads.
By removing all these spaces for cars, you could add back in green spaces. Houses with backyards can still exists, but they will be closer together. Parks will be closer and more accessible.
Plus you can design buildings to have green spaces, or at least support plants. Special consideration would be needed to make rooftop of buildings green, especially when you have to consider the weight and wind.
Space efficiency in urbanism is the key to reclaiming green spaces in our urban context.