In the desert Southwest, the very similar substitute, that serves all the useful purposes of river cane is the giant reed, Arundo donax, as well as the common reed, Phragmites sp.
The taxonomy is contentious among scientists. There is supposed to be a difference between the two, but it is not easy to distinguish and the size of the plant has been the biggest noteworthy difference. The problem with that is the size of the plant seems to vary more due to available water than to anything else.
The reason it matters, is because Arundo is considered an invasive non-native species, brought here by Spaniards, whereas Phragmites is accepted as a native species.
Actually, large reeds, cane if you want to call them that, were common, and many places in TX, NM, and AZ bear place names including the spanish name for the plant, Carrizo. I have also talked to archeologists who have found large diameter sections of cane dating to pre-columbian times, so whatever it is or was, it probably was native here and Arundo fills all the same niches and can be used for making arrow shafts, fishing poles, small boxes and containers, flutes, walking sticks, and you name it. It is also strong enough and was used to build quick shelters. It grows over 15' long and an inch or more in diameter, so it makes convenient tent poles or can be bent over to make dome-like buildings as well.
The old "canebrakes" of the stuff disappeared in most locations sometime after cattle moved in and grazed it down too often. I have found isolated wilderness patches of it, though, that were protect from grazing by cliffs and waterfalls. It is used as an ornamental, as well as an effective screen or windbreak in landscaping. It is beginning to flourish along the streams, since cattle began to be fenced out of riparian areas in the 1980s, and is considered a nuisance by many, as it impedes the flow of water to downstream water users, and may cause flooding by choking stream channels., so it is often cut down and poisoned by various groups.
It is great stuff, though, for all kinds of craft or survival uses.