I went through a nine-year period during which I owned one lens, and shot as often as possible at its optically optimum aperture of f5.6. Doing so taught me something: the optimum aperture for a particular lens is not the same thing as the optimum aperture for a particular image. In looking over my images from that time I saw how many images, but not all, would have benefited from deeper or shallower depth of field.
Having since added faster lenses to my kit I've enjoyed working with very shallow depth of field, but have noted a similar trend - the widest aperture of a given lens it not necessarily the one that best suits the subject (even if it does enable the shot in the first place by passing enough light to hand-hold the camera). I've often seen that stopping down to the f2.0 - f4.0 range improves an image by placing focus across the subject rather than on a detail, especially with portraiture. I understand this is a matter of taste, but that's mine.
I'm also a fan of "character" lenses and getting to know and use their subtleties across their aperture range is one of the joys of using them. As an example, the 75mm Summilux can be a challenge to focus as desired when used wide open. But even at close range, much comes into focus at f2.8 - f4.0 with pleasing out of focus rendering, all while maintaining its signature "soft but still sharp" look.