A weakened Russia is good for the world,
Just like the Arab spring was great for the world. Peace and stability came with the toppling of Gaddafi, Hosni Mubarak and the Arab Spring blossoming in Syria. Not to mention the peace and stability in the region after ousting Saddam Hussein.
Don't get me wrong. None of the names I mention are any good, but when you begin destabilizing a working situation, even if a bad one, you never know where you will end. That is why the Israelis keep ensuring Hamas gets funding to run Gaza.
Putin's request and interest seems very simple. He doesn't want NATO at his borders. He wants to maintain his ability to properly protect Russia.