Plain backgrounds help bring your subject to the forefront, but by removing the background, you lose something that can also be important: context.
When the background of a portrait or person orientated shot helps to tell the story or give more information about a photo, it needs to stay.
For example, you wouldn’t take a shot of the architect of a new building standing against a plain background; it makes much more sense to put his building in the background to make a visual connection with the viewer and the story you are trying to tell.
However, in these cases it is important to keep the background as uncluttered as possible and only include the elements that pertain directly to the story. For the above example, it would be irrelevant to the photo to have the cars parked next to the building included in the shot, as they have no bearing on the story that the photo is trying to tell.