The flexibility demonstrated with the axe is surprising and it could be used in the thrust especially if it had a spike extending beyond the axe head...and some had the addition of a concealed long spike in the haft. Using the left arm with shield to parry often enabled a decisive strike to the head or neck targets with the saddle axe in the right hand causing severe dental treatment for the opponent and worse...
I suspect that the Qajari period was responsible for the parade axe syndrome but that the axe proper ...as a battle axe and probably using very similar techniques as for the mace... was an ideal solution to heavily armoured cavalry impervious to sword and other bladed weapons but which the saddle axe was well capable. I get a headache thinking about that !
