The degree to which an elephant can manoeuvre in combat has been the subject of occasional debate. Now, with a live re-enactment (of sorts), courtesy of Zambia's South Luangwa National Park, we can see an 8-year old elephant display its repertoire of combat manoeuvres (https://uk.news.yahoo.com/survival-of-the-fittest--a-young-elephant-is-caught-on-camera-fighting-off-a-pride-of-lions-110350761.html?vp=1#FVzRqw7). (You may have an advert inflicted before the clip begins.)
Note in passing its relative helplessness against rear attacks but also its ability to charge through a water obstacle and turn practically on a sixpence (OK, on a 5p piece, double the face value). Notice also the extreme difficulty of inflicting a lethal or even incapacitating wound on a reactive elephant.
I wouldn't want to be in a tower on the back of that.
It could have its moments, certainly. One can see that sitting astride might have a certain appeal, at least in the absence of big cats.
Maybe 10 years ago, I remember Phil Halewood wrote quite a nice article on elephant maneuverability. Amongst other points noted was that elephants have a reverse gear, unlike other mounted types.... 8)