There were several different ways to do it properly- NV itself sets up at least a few.
But them getting nuked by Vault-Tec and dissapearing almost completely from the heart of the nation is very lazy.
NCR drains the last water reservoirs like Hanlon says and the famine OSI predicted hits them. The central government collapses and several smaller splinter groups wage a civil war over the remaining resources.
Legion wins at the Dam and pushes into the NCR outskirts. Frumentarii organize raids/ terrorist attacks like they did in Nipton and Searchlight, so the military focuses on protecting major or wealthy cities, abandoning the small ones to deserters/raiders/ Legion.
House or Yes Man kicks NCR out of Mojave. Kimball and Oliver are made scapegoats as House predicted. The military abolishes the democratic government and install an authoritarian state similar to FO2 ending when you murder Westin and Rogers. Some of the other cities want to preserve the democracy and decide to secede, while others get completely abandoned in order for army to focus on NCR heartland. Shady Sands prepare to deal with secessionists and free Vegas, but this time less diplomatically.
Desperate to prepare for the coming famine, OSI rushes research of Vault 22 plants and data. Major cities end up as wild jungles full of spore carriers, while the paranoid survivors torch the remaining farms and ranches, fearing that they'll too spread the infection.