Lots of feedback here. Good conversation. Here's my experience, and what I've learned from both training and experience.
I agree with Ron when he states that you have to turn your torso for a paddle stroke. That uses your back muscles instead of arm muscles. I don't agree that seating height will improve a paddler's stroke or vary the fatigue. Here's why.
When seated low in a kayak, there is much more to the fit than Ron has experienced. A kayak is fitted to the paddler like a pair of pants. First, width of the cockpit is adjusted with hip pads so that it is a snug, not tight, fit. A standard test of "snug" is, can you slide you fingers in and back out easily between your hip and the pad? That provides a snug fit so that hip thrusts to the side will affect control of the boat.
Another fit is foot pad placement. These can be too near or too far, and too wide or close together. Distance out is usually the first adjustment. A paddler's knees should be flexed up under the decks of his kayak, and his feet should rest nicely on the pads, contacting the ball of his feet. His feet should not be bent back uncomfortably, neither should he have to stretch to get firm contact. Specially shaped (cupped) pads are on the under side of the deck to both cushion and lock in the knees. This provides lateral control of the hull to initiate a roll, control about the longitudinal axis to dampen roll effect of wind and wave, and a great tactile feedback to the paddle. I've had the knee pads (also thigh braces) too far apart and it positioned my knees too far apart. This placed my hip joints too wide and a nerve was pinched somewhere. My legs would go numb.
With contact at the bottom of his butt, back, sides of hips, feet, and knees the paddler senses every twitch and move of his boat, and can instinctively move to add contol inputs for a smoother ride. An experienced kayaker will normally remain upright in his cockpit, while his boat can roll, pitch, and yaw underneath him. He can both feel his boat's movement, and move to add control inputs.
Now, paddling. We're basically talking only a forward stroke here; the power stroke that propels us forward and makes up the large majority of our strokes. I'm using, as an example here, a double ended kayak paddle, gripped with hands at about shoulder width. Paddle loom is straight, not cranked, and blades can be feathered or not, according to paddler's preference.
In a kayak cockpit that fits as I've described above, the paddler should NOT be paddling by flexing his arms. In fact, his elbows will flex only less than 5 degrees. (It is entirely possible to bend the elbows to a comfortable position and weld them there, never to move during the power strokes. But, a very slight flex is more comfortable in practice.) He turns to, say, his left, lowers the blade into the water up near his toes, and swings (rotates) his torso until the blade is about even with his hips. All this time, his elbows have not changed angle, except minimally, say, that 5 degrees I spoke of. Now, he rocks his arms to lower the right end of his paddle into the water up near his toes, while raising the left blade clear of the water, and does the power stroke on the right side back to even with his hip. His shoulders are parallel to the paddle at all times. He does NOT windmill his arms to paddle.
ALSO, while each stroke is being powered by the back muscles as the shoulders rotate, he is pushing against the foot pads with one of his legs. This is a part of the stroke with which, I think, Ron is unfamiliar. As you pull the left blade back, you are simultaneously pushing forward with your left foot and right arm. And, as you pull the right blade back, you are simultaneously pushing forward with your right foot and left arm.This does several thing for the paddle. Primarily, he does not have to lean forward with the effort of reaction to his paddle stroke. That tires back muscles prematurely. A forward leg thrust will transmit the power of the forward stroke to the boat. It also flexes the leg muscles to keep blood flowing and combat numbness in legs, butt, and back.
If a paddler only sits with butt contact, he has to strain forward from the waist to resist the force of his stroke. With a well fitted back rest, foot pads, and knee pads up under the deck, he has much more contact with his boat, and is less fatigued as a result. It is easy to raise the paddle from a horizontal position to nearly vertical to get a more forward component to the force of the stroke, but not necessary.