Yes, you are quite right about wing tip vortices, but you have also added weight to the overall aircraft weight, so therefore more thrust is required to push it along, which means more fuel, which in turn means more weight again, more weight requires more lift, which increases the amount of induced drag...
My point about winglets, is there are definately two schools of thought on them, from what I have read in articles, and I think this is proven by virtue of the fact that not all planes have them, eg. 747-400´, b737-7/800 yes, all the Airbus 320 family no, A340 yes, B757,767,777 no.
Explain that ?