The one case where the background may be a set
BetterPicAlmost every rule in professional portraiture pushes toward a plain background. Interior design is the legitimate exception.
Why the exception holds
The room is part of the argument. A designer photographed against a neutral wall has removed the evidence, and neutrality here reads as having nothing to show.
Where the exception stops
At legibility. A background rich enough to demonstrate taste is also rich enough to compete with the face at small sizes, and a headshot that dissolves into pattern has failed regardless of how good the room is.
The resolution is distance: enough separation between subject and setting that the background goes soft while remaining identifiable.
The inversion worth noting
In most fields the failure mode is a background that distracts. Here it is a background that says nothing.
What does not change
Contrast between hair and background, a crop matched to the display size, frontal light. The setting is allowed to be interesting; the face still has to be readable.