Time for another pair of feet to jump in:
If sharp at full opening, it should be sharp at all apertures. But since no lens is perfect, "sharp" is a relative term. The plane where sharpness is best will not be perfectly flat, but slightly curved. So best sharpness in the center doesn't mean the corners are as sharp as possible.
So we need more DoF to make the corners acceptably flat. We get this by stopping down the aperture.
A theoretical lens will have maximum resolution at maximum aperture, decreasing due to diffraction as the aperture is closed down. But since weære dealing with real-life bits of glass, our enlarger lens is not perfect. So there will be some point where DoF is sufficient to get a good sharpness over the whole easel, while not yet losing definition to diffraction.
Incidentally I just received four old lenses in the mail (I bought them for the shutters). They seem to have been used in some sort of repro setup, or perhaps printing. On one of them the aperture was taped stuck at f:8 - a reasonable value for the optimum working aperture for an f:4.5 lens in reproduction work!