I have a couple of concerns with this idea. The biggest is probably that it would be very difficult to design a rotation around building your choice of six different resources. If you have distinct builders, you either have a stupid amount of buttons, have weird complex combos for determining what you build, or have some sort of stance system. Remember, each class actually has mostly the same number of class actions since they unlock at level intervals. This means you actually can't give a class too many buttons, even if the rotations end up being simple.
Red mage suffers somewhat from this problem, in that many of it's skills are black/white clones and it only has two elements to balance. It gets around this somewhat by adding depth with a proc system, but it is still a very simple class.
Secondly, six summons sounds good but you need good reasons to use all six or or the unused one are just a waste of development time. People will just use whichever one give the highest DPS 99% of the time. They also aren't reactive since you need to build a separate resource for each so you couldn't, for example, quickly put out the healing primal if one of the healers goes down if you'd been building for your damage one.
Lastly, big summons are cool but there area already LoS blocking issues with Bahamut and he's barely ever up. If you intend these summons to be up ~50% of the time, they need to be as small, if not smaller, than players.
Honestly, your idea would work far better if you just had three primals. That would mean you could have enough button allowance to make the basic rotation interesting and few enough primals that it wouldn't be that hard to find a niche for them (Maybe single target, AoE and support?)
Edit:
The issue with this is that it would require tons of coding work to implement as there's nothing remotely like it in the game. I don't really get why you can't just have one summon button that summons the primal with the highest gauge.