Those are all good & valid points, which I do agree with, however, on the subject of being a blademaster, lets consider this.
The Aiel are well known for being the best fighters, generally speaking. Yet, al`Lan Mandragoran is one of the few wetlanders whom can, and is able, to defeat more than a couple Aiel in melee combat at once.
Also, look at every time that Lan has interacted with any other Warder. Remember, the warders are among the best trained swordsmen in all of the wetlands, right? Every time Lan interacts with other warders, they always treat him with the highest respect, and even defer to him. I believe that a large reason for this is that he is the best blademasters of all of the warders.