Are all lenses softer wide open?

[Dwig]

No, not true for all lens, but true for the vast majority.

Most optical flaws and compromises are more significant, and thus do more to reduce image quality, the wider the aperture. Stopping a lens down reduces the impact of these flaws and design compromises.

On the other hand, diffraction limits the resolution possible with any lens and the limit is greater the smaller the aperture (absolute aperture size, not f/stop with is aperture size relative to focal length).

These two combine to cause lenses to generally improve in IQ as you stop down to a point; the point where diffraction is more significant than the residual optical flaws, and then to get slowly worse as you stop down further. As a rule, most modern popular lenses will deliver their best images when stopped down 1-3 stops from maximum aperture.

In a few, somewhat rare cases the manufacturer will have chosen to limit the maximum aperture at a point where the lens delivers its best IQ. This happens only when the lens is very well designed and fabricated (read: high end, very expensive) and when this limited maximum aperture is still rather fast.