I am not sure that the reduction in ground effect is the primary objective of winglet.
And you'd be right. The reduction in induced drag only causes the aircraft to be more susceptible to floating during landing. Hardly can call that beneficial.
What winglets also do is help reduce tip vortices. Something that, in some cases, is necessary to keep spacing between heavies reasonable. By far their real benefit lies in the improvements to L/D ratio at high cruise speeds. Instead of regurgitate it, here: Understanding Winglets.
It's a PDF download, no author is given just a mention of using ideas from Fred George. As a brief background, Fred was (maybe still is, not sure) the chief test pilot and writer for BCA magazine. The article, at a glance, appears to be on target.