I've been lurking in this topic a few times and have had this same thought.
If they want to have a different way to recover MP, then it should be tied to job mechanics and not just random oGCDs like Fleche or Contre Sixte.
Black Mage already has it's whole system focused around the MP gauge, so there would be nothing to change there and as for Summoners, it could be added as an overarching mechanic that encourages you to use the summons, build up some sort of meter, and spend that meter on attacks that also restore MP. In my head I was thinking allowing them to summon Zantetsuken and weave that between their spells which does damage but also restores MP. As for why not a full Odin summon, remember, in FFXIV, The sword Zantetsuken itself is the primal, not the person themselves. So you summon the primal and use it's power, it is just done a bit differently.
