Your logic is present in a lot of economic thinking, but it is flawed as it assumes people are purely rational actors that make decisions at the margins. That is a classic Economics 101 assumption that turns out to only be true in theory.

In reality people are stubborn. We chase sunk costs and we repeat inefficient behavior because it is habit. People therefore won't necessarily choose to drive based on an evaluation of that individual trip. They will base it on things like whether they own a car, whether they have an unlimited pass for their local mass transit system, and simply what they did the last time they made the same trip. Therefore traffic can actually exceed where it was before as new and improved roads can lead to people buying more cars and people being less reliant on public transit.