If that were so, the canoe left to itself would be moving relative to the water (by moving downstream more slowly than the current, it would be moving upstream relative to the water).
No, it moves slower than the water, that's all. The wake is there.
It it had a wake, it would necessarily have motion relative to the water. Where does the energy come from to move it through the water like that?
You keep failing to address the simple point that there is no drag on an object moving at the speed of the current.
Not addressing? Does the meterological balloon not confirm the point?
I should add that is a very simple approach from a general methodological handbook. It is an approximation at best, and still shows the need for a driving force.
The force to drive the canoe comes from the water. Motion of the canoe through the water generates drag
ahead of the canoe, and that opposes the motion of the canoe. Because the energy or force required to move the canoe (and so generate the opposing force) comes from the same source, the river. Therefore, the drag will prevent the canoes from reaching waterspeed.
What you appear to be doing is taking "Gallileon Relativity" too literally. It is not a matter of 400 years of science, but a 400 year old idea that has been supplanted, in fact, by Einstein.
Not relativity, but his ideas concerning Brownian motion and Boltzmann's constant.
These insights are the basis of contemporary ideas on of drag, and those ideas say you are wrong. (Anecdotaly, thumbs bruised against the canoe's gunnels say you are wrong)
What proof would you need? I am not going to Wikki so that some idiots can post about it, but if you have an idea, then I will try to answer it.