So winglets increase span and thus aspect ratio, and can also improve the wing efficiency if designed carefully, so the CL distribution is optimised along the span. That makes total sense to me, particularly when one applies the induced drag equation!
This raises the quesion: why is there so much discussion ion apparently cedible online sources, stating that winglets reduce the strength of the tip vortices? Clearly they don't, they just distribute the vorticity in a more suitable manner along the span of the wing.