Or is it merely flow separation on the upper surface towards the end of the wing? The assumption seems to be that the air "leaks" from under the wing to low pressure above with sufficient rapidity to overcome or offset the forward flight speed.
You've correctly called them downwash vortices. They are caused by the air behind the wing—over all of its span—moving downward, while the air outside the span does not, which creates a pair of vortices that move downward at half the speed of the downwash (and somewhat slower later as there is more air below them in their way).
The air moves down behind the wing because the lift is an upward force acting on the wing, so the corresponding reaction force is downward and acts on the air, which, being free to move, accelerates downward.
This acceleration of air, however, requires energy (because its kinetic energy increases), and because energy is conserved, work has to be done to provide it. This work is done by induced drag.
There are several other ways to show, from basic laws of physics, that induced drag is a necessary consequence of producing aerodynamic lift that is proportional to the amount of lift and inversely proportional to wing span and dynamic pressure (that is density and square of speed). If the span-wise distribution of lift is suboptimal, it will increase the induced drag, but there is a known minimum for optimal, elliptic, distribution, and it is well known it can't be reduced below that.
The main issue with having huge wingtip vortices is vortex-induced-drag. Taking the starboard wing as an example, the air near the tip of the wing would move outboard, then upward, then inboard, then downward. So when the air hits the upper side of the wing the local flow is down and aft. This reduces the local AoA on that part of the wing, near the wingtip, thereby reducing lift and increasing drag. Also, the high pressure would have been higher and the low pressure lower if not for the vortex.
There is a second way of seeing this, from the perspective of energy. If we take the aircraft as the frame of reference, the incoming air and discharge air has the same pressure head (sufficiently far away from the wing), so if we ignore the compressibility of air all that's left is the kinetic head. The more you put into the kinetic head of the vortex, i.e. the more powerful the swirling motion of the air entrained in it, the less there is for the "normal" air just passing through and generating lift as if in an infinite-span wing. This means the bulk of the non-vortex air is slowed down more, which means more drag and less lift.