enjoying a football game with the elite.
I don't think that that's how people at that level operate. Putin, Erdogan, Xi are like the Tsars, Sultans, and Emperors of the past. The total degree of control over things within their borders, is so much more intoxicating a drug than being gladhanded by some western elected officials that will be out of office within mere years, and then likely will come crawling back to the Kremlin to collect some consulting fees for their new boutique advisory shop (Tony Blair, Bill Clinton, Schroeder, etc).
Putin likely doesn't see other Western leaders as peers. He's already one of the longest serving leaders in the world - up there with the likes of Mugabe and Dos Santos. He sees himself as an elder statesmen, that others should come to for advice. Don't think he's too worried about missing a G7 or G20 meeting.
Putin has long since moved on from things like money or acceptance at Davos. He's trying to write himself into Russian history as one of its greatest leaders.