This seems to be over complicated by mathematics. It is much easier to think of the hull moving through the water, the bow meets a resistence, which is translated as the bow wave. The stern is trailing in displaced water and is more free to move, so it gets blown downwind. That is the effect of weathercocking, it is what is actually happening. However, paddlers look towards the bow of their boat and see the relative movement of the bow only and think the bow is swinging into the wind (not quite the same thing, but certainly the same visual effect).
What is the skeg used for? To counter the leeward slip of the stern in the wind. That is what it is for.
What is a rudder for? Funnily enough, to counter the leeward slip of the stern in the wind.
How do they do this? Quite simply by adding a resistence at the stern, a lateral resistence to neutralise the effect of the resistence of the water at the bow. Not so complicated after all.
Now the relative merits of an over stern rudder (a well designed one, not a self tapping screw on afterthought):
The hull integrity is not compromised by grinding a great slot below the waterline, then laminating a stiff box in the flexible hull, so you end up with flexible sides and stiff centreline...below the waterline!
There is no intrusion into the aft hatch space to reduce your cargo carrying capacity.
There is no possibility of grit preventing the skeg from dropping - Sod's law dictates this will only ever happen when you need it the most.
The activation lines are the same, in that you need a means of activation, so we'll call that evens.
An overstern rudder requires no holes to be cut below the waterline. The hull remains as designed with no stiff/hard spots introduced.
The foot braces do not need to be compromised. Proper, firm footbraces can be utilised with toe control of the rudder angle.
The rudder out of the water syndrome can be overcome with the use of a properly designed blade - which trails, yes, but the angle of trail self adjusts according to the amount of rudder immersed and the forward speed. As your stern lifts over a wave the rudder blade drops, as the water pressure on the forward edge increases (through immersion) it trails to its natural position again according to your forward speed.
Rudder up in the wind - if it is a light wind so that you don't need the rudder, then there is insufficient wind to cause a noticeable effect on the balde area. If it is windy enough or the seas are so steep that you feel the need to deploy the rudder, then it won't be in the air, it will be in the water.
Going upwind, keep the rudder up - it is presenting so little surface area that it creates no hinderance whatsoever. - Antagonists of the use of a rudder because of the windage argument are quite happy to put kit bags on their decks....and thos kit bags don't create any windage? With a rudder, there is room in the hatch to put your kit below decks!
The use of a rudder is so misunderstood. People who do not use them think it is for turning the kayak, it isn't it is for PREVENTING THE KAYAK TURNING - we worked this out in the early part of my post. It adds a lateral resistence that stops the stern from slewing downwind. If you want to manoevre, you lift the thing up, put the kayak on edge just the same, and let the stern slew. You wouldn't try to turn a kayak hard with the skeg down - for the same reason, it is there to stop the stern slewing, so you lift the skeg up.
Paddling long downwind runs the rudder will win every time. The only way to test it is to put them on the same kayak with an open minded, independent paddler and try one, then the other. The rudder is more versatile and puts the blade out astern of the waterflow around the actual hull - in use and underway the rudder trails clear of the waterflow around the transom of the kayak, reducing the turbulence at the stern and allowing better waterlflow.
The question about drag - yes, you can feel the difference when you put the rudder down unless you spend a significant amount of money on profiled rudder blades. A flat blade works perfectly well, but the 1.5mm of frontal edge is enough to be able to feel it when it is down (plus the bit of flow along the blade sides). However, in calm or upwind situations there is no drag because it is up,out of the way and your perfectly smooth hull can glide through the water as intended. Coming downwind, again, if it is light airs, you don't need it so there is no drag (but there is with a raised skeg....all around the slot the skeg fits in, unless fitted with a flexible membrane either side like a draught excluder for skegs.)
Coming thrugh weed or rocks the rudder will just kick up over them....your skeg will drag in the weed and catch on the rocks.If you get long strands, like sargasso weed, around the rudder, simply lifting it allows the strands to fall off if they haven't slid off by themselves.
So, in effect the only difference between a skeg and a rudder, is how it is fitted. The reason for using it is the same. To add a resistence at the stern to counter the resistence of the bow in the water. That's all. The overstern rudder is self levelling according to the forward speed and other conditions. A skeg has to be manually fiddled with to get the required amount down.