Okay, this thread is about discussing how squenix could implement summoners from a practical standpoint, so lore issues can and should be ignored in this thread. Gameplay comes before lore.
At the moment I can think of 4 ways of having a summoner class but there can be a few more.
1. Old School Summoners (FF9 and before)
In this form, the summoner basically casts a spell, the aeon comes, does its job, and buggers off. The pros of this is they would be relatively easy to implement and balance, however the cons of this is you've basically got another generic mage class when it comes down to it.
2. Summoners as Blue Mages
In this form which is functionally very similar to the first, a summoner basically could learn how to use the powers of shiva and bahamut and the like as he would learn any other blue magic. So you would get Flare, Diamond Dust, etc as skills (more power longer recast?) that you can equip on your bar. However the drawbacks are the same as the first; you've pretty much got another generic mage.
3. New School Summoners (FF10 and on)
Basically you've got a pet class in this form. You call your beastie out and he comes and kills things at your side. Now this could be rather simple (equip a summon on action bar and use) or it could get rather advanced (it has its own action bar and skill set to manage, maybe its own equipment, AI settings and gambits, etc). The pros of this is you've got an Aeon at your side (but a weak one +con) and we'd have a real pet class in the game.
The cons of this is the summoner would be tough to balance. Do we have a weak Aeon? Do we only allow it to come out for a limited amount of time? How do we make it so it isn't OP compared to other classes? Can other classes have these pets too to make it fair? If we have pets, why not let us have Path Companions while we are running around too? What happens if we have both a summon and a companion with us ATM?
4. Transforming summoners
Has anyone else played shadow hearts? If not, in the first two games, the main character could take the form of a monster of some sort. So if they did this in FF14, you wouldn't call a summoned monster, you'd just transform into one instead. And it would have its own skill bar (customizable I hope). The pros are it'd be kinda unique, the cons are it'd probably end up as another group of classes for the devs to try and balance.
Then there's the possibility of a hybrid system of some sort. Like you could equip 2 shivas on your bar, one as an old school summon or blue magic which has a lot of power in one attack, and the other as a pet (I'd probably favor this system). And maybe for something like bahamut, he'd only be available as an old school summon (but if he doesn't do enough damage, takes to long to recast, or some foes dodge/avoid his damage, people are going to be pissed).