I would like to clarify one thing. Sharpness should not be confused with DOF.
The reason why most lenses appear sharper at f/8 is due to the provision of more DOF with stopping down. This will also definitely increase your level of perceived sharpness.
On the flipside, why lenses are generally soft wide open is because they are also not using the "sweet spot" of the optical circle of the lens, but rather the full optical circle. This also comes into play when using a lens for crop sensors, versus one for a full-frame sensor/film, but I digress. Stopping down uses the "sweet spot" of the optical circle, thus also giving rise to increased levels of sharpness.
So it is actually inaccurate to say "most lenses are sharp at certain DOF", because sharpness and DOF are really two separate measures. To look at DOF, one would look at focus charts, and the assumption is that with focus charts, the distance that is said to be in focus is really in focus, regardless of how shallow or deep DOF is at the aperture setting. But when you take a lens' optical performance in terms of the sweet spot in its optical circle, then stopping down will affect its sharpness, not so much directly due to the DOF rendered.