Nothing, if the winemaker wants to retain as much of the simple fruit flavor as possible. Barrel fermentation adds complexity. Think of it as the difference between biting into an apple and biting into a slice of rich apple pie. Fermentation helps extract a variety of flavors from the barrel that fully integrate into the wine. Aging in wood after stainless steel fermentation does add a layer of oak, but not the level of complexity.
Additional techniques impart a buttery taste and a creamy texture.
A balanced wine with lush, tropical chardonnay fruit, toasty oak, buttery flavor, creamy texture, a touch of spice . . .