Hydrologic studies have concluded that the low water level in the Colorado River is due almost entirely to massive drawdowns for irrigation. Same for the rivers feeding the shrinking Great Salt Lake.. Some modest elevation of water loss through evaporation into drier than normal skies which by itself would be no problem.
No doubt partly true. Water from Navajo Dam in New Mexico provides irrigation for crops on Navajo land south of the San Juan river near Farmington. Another recently announced project will take water from the same reservoir south through the New Mexico portion of the reservation to Gallup, New Mexico. This is because the tribe claims senior water rights to the river. Additional irrigation occurs along the Colorado river in the Grand Junction area and eastward. Finally, reservoirs on the west side of the continental divide provide water for the Denver metro area on the east side.
Regarding droughts, they are thought to have caused the abandonment of inhabitants of Chaco Canyon, NM with geological documentation of a fifty year drought that began around 1130 AD.
Irrigation to grow more food? Tens of millions pouring into our country require more and more food.