There are a number of people who do so. I know several private investigators, people who work car repossession, police officers, people who serve summons for court, etc. These can be dangerous professions, and many/most of the people who have those types of jobs carry a firearm.
It's also somewhat dependent on your state. Here in Texas, I would wager that a double-digit percentage of cars on the road are carrying a firearm at any given time. That's probably a lot different than California or New York.
But regardless of your philosophical stance on whether people should carry a gun or not, I thoroughly appreciate the OP looking to safely carry his. Making sure that your firearm is under control and secure at all times prevents it from being stolen, being found by a child, or being lost. We always hear the phrase about "responsible gun ownership" -- ensuring the safety and security of the weapon is one of the hallmarks of a responsible gun owner.