The answer is jobs, and privacy.
The more roads, the more opportunities your citizens have access to. Also, those same people don't want to live in Apartments that they'll never be allowed to own, packed like sardines in a population dense building.
So, roads allow them to have their own houses out in the suburbs - and the more of them, the faster they can get to their destination. The faster they can get to their destination, the further out they can move. This also supplies businesses with a wider reach of the population for whatever their needs are.
And people don't want to waste an extra 45 minutes getting to their destination by waiting on public transportation. We're a population of people who - when we want something done - we do it now. Delays are unacceptable.