This is one reason to have multiple design models for games. When all you have is one model, one theory, around game design, you miss aspects of games. GNS theory may tell you how well your game appeals to desires for G, for N, or for S. It doesn't help you meet other desires the players might have. Today, this would include identity desires, but won't be limited to that.
As a highly relevant example of today - GNS theory doesn't inform you about design theory around making a game appealing for remote play.