Thats just a question of how you would design the mechanics around the job itself. Every class/job in FFXIV is possible. Im not a game designer to think about how a PUPP would be a great new job class for the game. But I mean a Ninja could also be an other monk because he uses duel wield for damage.. but NIN has its own gameplay mechanics that make NIN a legit class ingame.
same for RDM instead of using just only BLM and WHM spells (like the RDM iN FF11) he has its own spells and gameplay mechanic in FFXIV (balancing black and white magic out in order to boost your melee attack etc.). They could even make the pets of PUPP completely different. Instead of having endless MP for the mage pupptets they could implement something "heat-o-metre" bar .
http://originaluncledougies.com/asse...fc793e30d7.png
So if you command your puppet to fullfill several powerfull skills like stoneskin or cure III it costs a higher amount of points that fill your puppet's bar and increase the chance of overheat. So if you use too many special abillities your automaton overheats and the puppet is stunned for a several amount of time. (overheat was also a thing for PUPP in FFXI) The bar could cool down overtime automatically. Making the skills of a puppet more powerful than the summoners pets spam basic attacks (and the possibillity to heal or buff), but also limiting their usage by a overheat bar.