You do understand the concept of erosion, right?
Well, the river DID make the canyon, not a mythical globle-girdling flood, but there is a grain of truth in what you say.
The canyon was formed by THOUSANDS of large floods OF THE RIVER.
Of course now, there are so many dams and so much irrigation water taken from the river that there isn't all that much erosion going on at all, but even if you'd visited the Grand Canyon in, say, 1900, most likely the day you visit, the river wasn't eroding much at all.
Basically, for any given river, almost ALL the erosion of its valley occurs on the few days a year it's flooding.
In the case of the natural Colorado, basically all of its erosion took place during a few days or a few weeks when the Rockies snowpack melted.
The rest of the year, there's basically no erosion at all.