Increased vehicle traffic is a bad thing. You want to induce demand for other types of transportation.
There is a finite amount of people willing to move to X city / a finite number of jobs for them to support themselves.
But I have to admit that adding another lane does allow more people to use the road. Even if everybody ends up stuck in traffic again, overall more people are able to get to work or wherever they want to go.
That being said, I still think that with correctly priced externalities, and when offered the choice, that most people would prefer to bike or take the train.
If your roads are jammed, some people who want to take trips on them will take other means or abandon the trip. If additional lanes are built, trip capacity increases, and more trips are taken. Sometimes the amount of supressed trips is such that traffic jams continue to the same extent as before... but that's unusual --- when Caltrans widened the 405 in west LA, morning and evening jam duration was significantly reduced; but population growth continued and trip demand growth continued, and the jam duration grew.
It's the same with housing. A lot of people would love to live in (city you like), but can't because it's too expensive or too hard to find a place. It would take a lot of construction to change that, but incremental construction is still brings supply closer to demand; even if the difference is hard to spot.
There's certainly places that have sufficient roads that there's rarely a traffic jam, and that have sufficient housing such that it's affordable enough for all who want to live there... those places tend not to have a lot of traffic density and not a lot of people density either.
The most effective way to make housing affordable is to make the city undesirable to live in, but that's not typically a popular method. It also tends to make traffic better, too.
If suddenly a city were somehow flooded with supply of homes, wouldn't more people decide it now makes sense to move to the city, and prices would rise back up?