This is true but the main concern with compression loads is buckling, which generally happens well before the material yields to normal stress. This means that

This is true but the main concern with compression loads is buckling, which generally happens well before the material yields to normal stress. This means that compression members need to be much stiffer in bending, and so generally bulky and geometrically large, with a big moment of inertia. Whereas tension members can basically just be wire rope. Wood can easily be built up into a much larger cross-section than steel for the same cost and less weight, so it makes sense to use it for compression loads.