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
cost of living - can be solved if its social housing provided by the government and/or assigned by need and/or there is a restriction that the properties can only be owned by individuals.
traffic - if everything is a walkable or cycleable distance traffic should be alright even with poor public transport. Although if we are trying to right the wrongs of bad urban planning you’d like to think public transport, green spaces, utilities and amenities would be well planned out in this scenario.
homelessness - homelessness is not directly related to cost of living, its more related to lack of a social safety net and social services. The cost of living rising just exacerbates the issue.
That could alleviate those problems, but I doubt it’d actually solve them. Not to mention, they could also get worse: