As a programmer, I'd say they are not! Design is a separate skill from implementation, and regardless of the skill the programmer has at coding, their skill at game design can be quite variable. This is not even getting into the fact that not all programmers even know how to code games since some of them don't really focus on that area of coding.

However, when it comes to indie games, programmers (and game programmers especially) may be more willing to design games that require more complicated or customized game mechanics because they might tend to have more confidence and skill to implement and debug those mechanics. I'd imagine that likewise a skilled artist would be more willing to design a game that leans heavily on its art assets to create its appeal. And a music composer might be more willing to design a game that uses its sound assets to best effect or in some innovative way.

In the end, I think anyone can be a good game designer if they have some experience playing games and can deconstruct for themselves the mechanics that make those games enjoyable for themselves and others. But in order to implement the game, they're going to need to have other skills or enlist the help of others with those skills.