Why do you think the Soviet Republics rejected the concept of unity and declared independence once the Communist Party lost control of the USSR?
The former Soviet Republics had little in common with each other even during their years as members of the Soviet Union, and there was essentially no common ground between them which would support some type of national union. A classic case is the Republic of Georgia, the birthplace of Soviet dictator Joseph Stalin. The people of Georgia speak their own language, typically used the Roman rather than the Cyrillic alphabet, and although orthodox Christian, had their own church. They were forced into the Soviet Union by Stalin who tried to gloss over these differences. There are also substantial ethnic differences between the former Soviet states. Each state understandably wished to preserve its national identity apart from the others. It might have been possible for these states to form something of a voluntary united union, similar to the United States had they originally been voluntarily associated with each other. Sadly, the Soviet leadership had sought to abolish national identities and create one great Union, and had conflated peoples and nations of separate identities against their will. By doing so, they precluded any possibility of unity after the fall of the Soviet Union.