Low-traffic routes may smell better, sound better, and look better than busy roads. Vehicular cyclists like myself often find such routes enjoyable and may choose them if they have the time. I personally have invested scores of hours advocating improved street connectivity in fast-growing suburbs in order to facilitate the existence of pleasant alternate routes.
This is irrelevant to vehicular cycling, however, unless one proposes alternate routes/facilities that require operating contrary to vehicular rules. In such cases, self-described vehicular cycling proponents will generally prefer to use the busy street in the normal vehicular manner.