The "higher ground" ploy would only work to a peaceful end if it went like this.
Obi-wan: It's over Anikan! I have the High Ground!
Anikan: Dammit! You beat me at everything! *throws down saber and cries*
It was a taunt. Anikan could've easily repostioned himself some other way, he was so consumed with the darkside he went for the whole gig. I just think it's funny how Obi-wan pulled the higher ground act when he knew good and well that he has won some tight battles from a lower position. Not only against Maul but Grievous as well. Though we all know Maul had his chatbox up anyway and Obi-wan lamed him.