The biggest reason, perhaps, is that cottonwoods need it to reproduce. Their seeds fly in the late spring wind, about the same time the river used to flood. The seeds last only a relatively short time and need flooding to germinate. There wouldn't be a bosque if there hadn't been flooding.
Cottonwood trees are the anchor for the bosque ecosystem.
But they are aging, and the absence of flooding has led to an absence of new cottonwoods. I don't hold out an awful lot of hope for the bosque unless there's some selective flooding. But flooding has other benefits to the Rio Grande environment as well. It clears, buries and helps decompose fire fuel. It moves fertile silt into the forest.