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True. But I guess moving the King is about the worst thing you could do anyway, and would only be done to move it out of enemy check. In which case the opponent cannot move it back, as this would then put it in 'friendly check'.

This is a bit similar to variants where you are allowed to pass your turn (e.g. Janggi, and Chu Shogi when there still are Lions). If both players decide to pass every turn, the game makes no progress. But usually there is something better to do than passing your turn.

And this again is similar to shuttling your Knight between g1-f3 while the opponent does it between g8 and f6. It is always possible to have no progress, if neither player wants progress. The important thing is how easy it is to make progress in case your opponent doesn't want any.