That could alleviate those problems, but I doubt it'd actually solve them. Not to mention, they could also get worse:

• Cost of living -> Could actually be driven up. Stuff always tends to be more expensive in dense metropolitan areas. Big corpos and rich assholes would buy up as much real state as possible.
• Traffic -> Without public transportation, this can actually get worse. The distances might be smaller, but the amount of people wanting to get there increases.
• Homelessness -> directly related to cost of living. Having lots of places to live in that you simply cannot afford will force you to live elsewhere