When I grew up "running gear" was a term used to describe the four wheeled frame and tongue of a farm implement that would carry either a flat rack for hay or a gravity dump wagon body for hauling grain. Here on the Airforums, it is a term often used as a tool to compel someone into buying something or cast uncertainty and doubt on their trailering experience.
Sometimes it is used to explain popped rivets, sagging outriggers, belly pan that is coming un-attached, cracks in interior or exterior skin and a few more things. I would say that the term "running gear" is a bit misleading. What we are really talking about is the proper balance of the rotating mass. The tires, wheels and hub and drum assemblies. Some people install "Centramatics" in an effort to keep their wheels and tires in balance continuously. I don't own them, but I think they may serve a useful purpose. High quality wheels and tires that are balanced dynamically (spin) are a minimum requirement. If you are truly looking for a complete balance of the rotating assembly you must have the hub and drum or hub and disc balanced at a machine shop that does precision machining as well as having the wheels and tires spin balanced at a tire shop such as Discount tire. People that sell Centramatics will tell you "Install Centramatics and be done with it" The same people will tell you that "Centramatics can only go so far to maintain balance" So that is why I believe if you are looking for completely balanced rotating assembly, the hubs must be balanced as well.
I just have my wheels and tires balanced at Discount tire annually.