What makes me think that? Simple mathematics! Since there are 22 players and one is replaced each day, the average HAS to be 22 shows! Well, near enough. Technically it'll be slightly less because occasionally players fall ill and leave without playing, and also the first 21 players won't have been there as long, which makes a tiny difference (and getting tinier as time goes on). But basically, 22 shows is the average.
Yes, some people have to wait longer than 22 shows, but some people wait fewer than 22 shows. It all balances out, and the average is 22. And the average cannot get higher than that. Think about it: if someone goes on for 31 shows, then someone else (probably several other people) will need to go on earlier than their 22nd show - otherwise they'll end up with shows where nobody plays at all! That would be kind of interesting, actually...