I'm not so sure that landscapes are usually taken with "big" apertures. However, there is a reason large apertures make sense in some situations.
When there is nothing close to the camera in the picture, as can be the case with landscape shots, most of the scene will be at infinity focus. In that case there is no benefit from a larger depth of field, so you can use the sharpest setting for whatever lens you have. This is usually a couple of stops or so down from wide open.
Diffraction goes up with smaller aperture, but lenses aren't perfect, and wide open will be a compromise between different parts of the design. Usually a couple of stops down from wide open reduces abberations and other quality problems with the lens full open, but is still a wide enough aperture that loss of sharpness due to diffraction is below other sharpness limits.
This will be different for very high quality, and therefore expensive, lenses. Those will be better relatively at wide open, so you want to stop down less for the best sharpness.