When you’re flying along a flight plan using your autopilot with the nav source engaged, you may think the heading bug is insignificant since it is not in use by the autopilot. But while the heading bug may not be active, it is worth keeping it centered as you fly along.
With the heading bug centered the display looks more streamlined. Unless you expect to turn to a specific heading, it simply makes more sense to have the heading bug on the current heading. And this way, once you engage heading mode on the autopilot, the airplane won’t turn in some random direction. Instead, the airplane stays stable until you turn the bug to the desired heading.
Being in the habit of having the heading bug centered is useful when you get an unexpected vector by ATC or need to amend your flight plan. At that point, you can simply activate the heading mode on the autopilot without having to first think about where the heading bug is pointing. Also, if the autopilot for some reason gets disengaged, it may make sense to initially use heading as the data source for the autopilot. Knowing that the airplane will continue in the same direction you’re flying makes that transition easier.
Most glass panel avionics have a button that centers the heading bug when you push it, so keeping the bug centered is effortless. With round gauges, it takes a little more effort. But it’s better to put out that effort when you’re casually flying along than needing to do it when something unexpected happens.