It does stay in the channel, which is a record of the meandering course of the river. Cf. Horsehoe Canyon in Utah:
Staying in the course is a moral or political argument. If the god of Genesis wanted water to cut through meanders, He would surely have made it so {poof}.
Of course it stays in the channel. It CUT the channel. The river wandered around, always flowing in the easiest direction possible. Water isn't intelligent, it just flows downhill. Hard rock on one side of the flow, soft rock on the other side, it will erode the soft side first, and go that way. It flows downhill.
I don't think that we disagree here. The Grand Canyon was cut by the river that runs through it, not by the imaginary flood that supposedly flowed over it. If there was such a flood, it would have flowed around it: It could not have flowed over it.
According to the whole "flood theory" nonsense, the Grand Canyon was cut by waters flowing over it, which would have been impossible had it not existed in the first place, for the waters to flow through. Otherwise, the water would have flown around that particular hill.
The only logical conclusion is that the ground was rising as the water was flowing, and that the water chose the easiest way through. That way is called erosion. It happened simultaneously. The hill rose, and the water flowed in the only direction that it could; downhill. The water cut the Canyon. No great flood, just slow and simple. The hill rose, and the water adjusted. It never left the canyon that it was carving because there was nowhere lower for it to go.