Why not paddle with a plank?

I've been thinking about how to explain the basics of the classic paddle shape for a while now. A really simple way to understand all of it's curves and form. And today by accident I thought of a good way.
I had loaded the canoe on our car getting ready to paddle to work. It's a 10 min drive and then a short portage and a short trip on the sea out to the island where I'm working at the moment. So I portaged to the shore. Put the canoe in the water and was just about to paddle away, when I realized... I forgot the paddle at home. So I had the option to either walk to the car, drive home and get it and come back.... or find something else to paddle with.

Well, what are the requirements for something I could paddle with?  Just a stick would have been enough. If it's long enough it can propel the canoe forward and even simple steering is possible. But it's not easy to hold, since it has no flat grip neither horizontally or vertically. And because the part in the water is also round it won't get a good grip in the water. So I went the more sophisticated way and took a plank I found lying around. This gave me a flat surface with both a horizontal and vertical area to hold. And a flat blade for better grip in the water. But unfortunately the only plank I found was too short, just a little under a meter (3 feet) long.
Either way I decided to head out with this. Paddling with such a short "paddle" was very exhausting for the wrist because I didn't get the leverage of a longer paddle, so had to press harder.
When I arrived at the island I found a longer plank for the trip back. Now this I think is the minimum for comfortable and efficient paddling, a thin plank in good length. From here on it's mostly luxury adjustments to make paddling more comfortable.

My next concern was that I couldn't do underwater recoveries. The plank was too thick so the underwater recovery would turn the canoe toward the paddling side and slow it down. So I had to lift the rather heavy plank above water every stroke. This could easily be adjusted by sharpening the edges with an axe. And to lower the weight the whole under water area could be made thinner. I didn't do this as I was just paddling a short distance. But if I was on a trip and lost my paddle I definitely would. Assuming I had an axe or knife with me.
Next problem was the middle part of  the plank. It's too wide to get a good grip around and the lower hand comes too far from the center for good J-strokes using the gunwale as leverage. This is the reason for the shaft. This too, would be quite easy to do with an axe in an emergency.

Now at this point all other modifications are pure luxury. Except one. I mentioned the curves of the paddle in the beginning. They are not just there to look beautiful. A good even curve in the transition from shaft to blade adds a lot of strength. Same from shaft to grip. The reason is that each fiber in the wood gets an underlying fiber that stretches further. Imagine a blade which just has a 90 degree transition from the shaft. When you paddle pressure is put on the sides of the blade. A lof of pressure is put on the "corner" closest to the shaft. It will be forced to bend backwards and the point that bends most easy is in the 90 degree corner. Eventually it will bent too much and crack. By having an even curve the "bending point" will be split up over the whole area and allow the paddle to do a smooth bend.
To try and explain this I made a simple (but ugly) drawing in illustrator. Click to see it bigger.

Well, to summarize it. I think this thought process is how the paddles have evolved. The very first watercrafts, maybe just logs, were propelled by sticks. Someone noticed something wider has better grip in the water, and from there on it just kept evolving into what we have today.

For more in-depth read about paddle design see some of my first posts:
Open canoe paddles 1: The paddle and materials
Open canoe paddles 2: The shaft
Open canoe paddles 3: The grip
Open canoe paddles 4: The blade