Because, at higher frequencies, the flow of current in the conductor is almost immaterial, as much of the energy flows in the space around the conductor instead. This space needs to be constrained (by pouring ground around the traces) to achieve consistent and useful transmission line impedances, and prevent the energy from crossing into every other single conductor on the board, and outside the board (radiated emissions).
Even at DC, you might still want the increased coverage due to costs (less etching to do -- however, less copper to recover from the etchant, so if this vanishingly small difference comes up in your cost analysis when it's time to order a million boards... maybe look into it), slightly improved strength and stiffness (especially for heavier boards), and much improved thermal conductivity (good for dissipating power on SMT designs, even when the copper isn't directly connected to the hot parts).
Although it helps to have a copper pour, it helps even more to stitch the copper. Just because the copper is connected, through some roundabout path, back to ground, doesn't mean that any given point is locally grounded -- traces and pours exhibit inductance at higher frequencies. Shorting across all of those paths, by pouring the top and bottom sides, and stitching with vias, is the best way to ensure solid performance. A board made in this way can be almost as good as one with internal ground layers!
Tim