It does stay in the channel, which is a record of the meandering course of the river. Cf. Horsehoe Canyon in Utah:
Only if you don't read topographical maps. The rim of the Grand Canyon is the highest point in the area, by thousands of feet. For the canyon to be cut by a catastrophic flood, the water would have had to flow uphill for thousands of feet in elevation. Water doesn't do that. It doesn't go for the highest point, it goes for the lowest.
If a huge amount of water would have suddenly been flowing in the area, and the topography were the same then as it is today, with the exception that the Grand Canyon did not exist, the water would have flown around what would have been a small mountain, not over it.
The only explanation that "makes sense" is that the land in the area was gradually being upthrust, as the water flowed through it. Water flow, upthrust, and erosion were at an equilibrium, to some extent. That the Canyon wanders rather significantly is indicitave of the different materials present, in that some materials erode in water faster than others. If the channel was always the lowest point, the water would have stayed in the channel. Otherwise, it would have gone around.
It does stay in the channel, which is a record of the meandering course of the river. Cf. Horsehoe Canyon in Utah: