Stopping down is suggested because many lenses are considerably less sharp when wide open. This does not change on a crop-camera, since it is a property of the lens. There is however for most lenses a difference between center sharpness and corner sharpness. Most of the time, the center sharpness is substantially better than the corner sharpness.

The difference between a FF and a crop camera is shown in the diagram below. A crop camera uses a smaller proportion of the lens. This means that when the lens has a bad corner sharpness, this becomes less relevant for a crop camera. Therefore if you have a lens with an excellent center sharpness wide open, it might become less relevant to stop down on a crop camera.

As a final remark you have to decide if corner sharpness is really an issue when shooting wide open. Most of the time when you are wide open you are shooting objects with an out of focus background. When this is the case, what does it matter that your lens has bad corner sharpness wide open? Absolutely nothing.

So, to answer your question, it could still be necessary to stop down with your crop camera, but depending on the center sharpness of your lens in relation to its corner sharpness, it might become less important or even unnecessary.