If you build more dense and closer to work and shops, people can travel smaller distances. Public transport, walking and biking will become viable alternatives, resulting in fewer car trips. You could have less traffic when planning it well.
We still need to build ways for all the new people in those new suburbs to get to the rest of the city. Building to dense neighborhoods is a lot cheaper than father out ones (because we need a lot more distance to get them) As a bonus transit works better as you become dense.
- LA is already building various large expansions of public transit, as well as walking/biking infrastructure.
- Generally the shops basically come along with the housing. "Activating" the ground floor - putting retail or other public uses into the ground floor of buildings that are residential above is standard practice when building those taller residential buildings along main arteries, on busy corners, and so on.
which suffers from many difficulties and cost overruns because of existing layout.
I think it would be more cost efficient to build another city/town nearby from the ground, and people decide where they want to live given differences in cost and lifestyle.
That is ignoring the fact that in our perfect city above, just a few years later we will discover something new we forgot to account for and now our city is imperfect.