Yes but that isn't actually what happens because the use of a street or road isn't by one car from A to B but by the continuous use over time across a section of the street.
Say you had a single 1 mile arterial in a city, and it's the only way of getting from one half of the city to the other half. There are few points when a cars are "off" of it (except maybe late at night) - the rest of the time it is a near constant high speed flow.
You're not wrong to say that it gets any given car off the road quicker, but that is if you're focusing on the one driver's trip, as opposed to focusing on the use of and experience of being at that section of road. If it was an old town which had its main street become a high speed arterial, you now have an experience for any pedestrians who might want to use the (probably few remaining) stores along that road be not unlike walking along side a freeway - unfun and dangerous.
By focusing on any one driver's trip experience, and not the street experience, you're essentially damning the street experience for the potential sake of some extra time saved (if its across a city, perhaps on the order of 10 or so minutes).
Of course when you have nothing on the street worth being around (like most of El Camino Real), you want to get passed it ASAP. (SF problems are a whole other hairball of outside commuters plus residents who insist on using cars.)