Earlier quoted context omitted.
Elo is zero sum. Each point gained by one player is lost by another. It follows that the mean elo is always exactly equal to the initial elo assigned to new players before they play any games, and can't change over time. If the highest ranked player are higher elo than before, the lower ranked players must be lower elo.
>Elo is zero sum. In a closed, static pool only.
Right, but you have to give the new players some rating, and as long as that number remains constant it will also be the mean Elo. Therefore, "new players entering the pool" can't cause a rise in mean Elo. As for lower rated players leaving, that could indeed raise the mean (assuming you stop counting them in the average), but that changes the point from "players have gotten better because of AI" to "worse players are more likely to just give up on chess because of AI", which is a significantly less optimistic picture IMO.