Games of the top players are watched by huge amount of players (especially in tournaments). It would be nice for lichess to automatically request a server analysis for such top games, right after the game finished.
I think you misunderstood me. People actually click the button pretty often. Check the games of the current top marathon player: lichess.org/@/galbijjim/all and you will see that more than half of his games are analyzed (and not by him). BTW a lot of new users do not know what is computer analysis.
My suggestion here is for lichess automatically analyze the games of such players. Maybe even in a realtime. The game is finished and the analysis is already available for everyone to enjoy.