Go is a turn based game without this feature (or bug?) because you aren't forced to move, you can instead pass. Both players passing in a row implies neither player thinks they can improve their position and the game ends.

I think zugzwang makes chess endgames richer - the fewer ways you can make a draw, the better, in my opinion. Maybe that's less appealing in go because games can go on for so much longer? At least in 19x19.