Really, I think it's a fascinating idea with a lot of potential. I'm also glad that the eventual summoner class will still be around with access to other spirits, 'would have been disappointed otherwise (also, remember there's more than one traditional FF spirit for certain things. We could say, have Quetzalcoatl as the primal of lightning, and Ramuh as the spirit called on by individual Summoners).
That said, I think the 'once you've got it, you have to use it inside a week' element is a bit disappointing. 'Guarding it' so it can't be used against you is an interesting strategy in and of itself, and lends more personality to free companies.
I realise there are balance issues to that, but at the same time, a time limit strikes me as very lazy - surely the better way to go about it would have been to make the primal one of the most difficult things about a free company to maintain and the easiest to lose in the event of an attack. Say, having to maintain a poorly defensible temple in order to hang onto it.
If nothing else I hope they examine that issue down the road.