When a country dissolves, merges, or suffers some other major changes, it's customary that the new country which emerges from this process inherits the rights and duties of the former - for example, international debt but also membership onin international organizations and treaties. When a country splits, some negotiation is needed in order to decide which of the new countries inherits, or other some kind of agreement.
Russia inheriting most of the status and international positions of the former USSR is nothing strange. It was a pretty straightforward process. As for why the chance of "getting rid" of them wasn't taken:
Nobody wanted to "get rid" of them. The security councilSecurity Council is an organization of peacekeeping. Notwithstanding all its defects, which are many, it's better to have Russia onat the table than not. The Security Council, just aslike the UN in general, gives a pretencepretense of "international law" to the decisions it agrees upon. A security councilSecurity Council with just France, the UK, and the USA is not a UN Security Council: it's a NATO Council, and you can count on it that Russia and China would make their own versions. In the end, the United Nations would split into several Not-So-United Nations.
China would have vetoed any initiative towards the expulsion of Russia -, knowing they could be next.
If you start kicking permanent members out of the security councilSecurity Council, maybe some countries will start thinking about why there must be permanent members at all, with veto power, or why they shouldn't be one of them. That's a can of worms the current permanent members would rather leave closedunopened.