We already do this. In Colorado there are over 50 "Transbasin Diversions" that move water from one river basin to another. Most of them transfer water out of the Colorado River Basin to the east side of the continental divide, usually the Arkansas River or South Platte River Basins. California also does this on a vast scale to move water from the wetter north to the drier south parts of that state.
There are many issues with transporting large quantities of water vast distances. From legal (it is illegal to transport water from the Great Lakes to outside of their basin), to physics (water is expensive to pump up and over mountain ranges and building tunnels is incredibly expensive.
Basically, just like there are only so many places that it is cost effective to build dams or pumped hydro electricity storage, there are only so many places that it is cost effective to build pipelines.
There are many issues with transporting large quantities of water vast distances. From legal (it is illegal to transport water from the Great Lakes to outside of their basin), to physics (water is expensive to pump up and over mountain ranges and building tunnels is incredibly expensive.
Basically, just like there are only so many places that it is cost effective to build dams or pumped hydro electricity storage, there are only so many places that it is cost effective to build pipelines.