We all already have the ability to be puppetmasters to some degree. If you wear the Mammeteer title then you unlock additional actions when interacting with mammet and wind-up minions. The one I remember is:

/handover will make mammets and wind-up minions eat out of your hand

This doesn't work unless you have that title up. I think there were others like this, but can't remember them off the top of my head.

The concept of PUP/MAM definitely already exists in XIV, so it's not a stretch at least in lore terms that a puppetmaster/mammeteer job could be a thing. I too would like PUP/MAM to be in-game since I was a PUP main in XI but I'm not sure how well it could be implemented in XIV.