My understanding of the physics of the wake is this:
The aircraft's lift force is matched by a transfer of momentum downwards to the airflow in the wake (Mr Newton), which is what drives the vortex. In level flight, the rate at which the momentum is transferred matches the aircraft's weight, and is inevitably associated with some energy imparted to the air: mostly kinetic energy in bulk flow, with some thermodynamic effect from changes in pressure, both smoothly and in shocks.
By minimizing the kinetic energy given to the wake, for a certain amount of momentum, you reduce the rate at which energy is lost to the bulk airflow (induced drag) for a certain amount of lift.
The amount of kinetic energy imparted to the air in the wake depends on the product of its density and the speed-change-squared - while the momentum transferred depends on the product of the density and the speed-change. The key goal is then to minimize the average change in speed in the airflow in the wake, especially of the fastest-moving parts of the wake - the core of the vortex, where the speed squared term is most significant.
If you can reduce the average speed of the same mass of air in the vortex, by making the extent of the fast parts of the vortex less, as suggested in the Boeing cartoon above, or otherwise, using a fence, increased span, raked tip, winglet etc., then you're making the owner happier.
It's not dissimilar to the efficiency of a jet/propellor - you want to move as large a mass of air as possible, by as small a change in speed as possible, to get the maximum force from the minimum amount of energy expended.